When light, an electromagnetic phenomenon, encounters a material with a high degree of reflectivity, we have observed that it will reflect according to the law of reflection from the surface of the material, that is, from the boundary between the material it was traveling in and the material with a high reflectivity. But those surfaces can be shaped in many ways. Let's explore what happens to light as it encounters surfaces of various shapes that can reflect the light back in the general direction from which it came. In this lecture, we're going to begin to explore the concept of images, and we're going to use as the vessel in which we explore images, the device known as a mirror. I'll introduce the terminology associated with both of these ideas, and we'll see examples as we go through the lecture of how to understand mirrors and the images that they produce. The mirror with which we're most familiar is likely the plain mirror.  Mirrors are very good reflectors. They're never perfect, but they're highly reflective. They reflect much of the light that strikes their surface. And as you can see from this picture here, there is the possibility, under these conditions of nice specular reflection, for an image to form. If we were this vessel that's sitting here on the ground looking at ourselves in the mirror, we would see an image of ourselves that moves when we move. It steps forward closer to the surface of the mirror when we step forward closer to the surface of the mirror. But what's interesting about the image is that it appears that our twin is on the other side of the surface of the material. Now we know that physically that's not possible. It can't be that our mirror image is physically, literally on the other side of the material looking back at us. Rather, what we're seeing is an optical effect created by where the rays of light reflecting off the surface appear to converge in space. So a plain mirror offers us a doorway into a larger discussion of reflection and mirror surfaces and how different surfaces will cause different kinds of images to form. When we begin to talk about images, it helps to define some basic terminology. For instance, what is an image? Well, an image is merely a place in space where your eye perceives light rays to be emanating from. This point in space represents the location where light rays are focused by the mirror. So taking the example of the plain mirror, which we'll explore with some drawing in a moment using the law of specular reflection, you can already pick a point on your body like the tip of your nose and look at it inside of the mirror. And of course you'll see the tip of your nose reflected in the mirror.  They're reflecting off the surface of the mirror in many directions.  If you pick a bunch of those rays and trace them back behind the mirror where they appear to converge, that point of convergence is the location where the image of the tip of your nose will appear. We'll do this in a drawing way in a moment so that it better illustrates this point. But you get the basic idea. An image is merely a location in space from which reflected light rays appear to be emanating, or when we do lenses refracted light rays appear to be emanating. What is a focal point? Well, the focal point is that point. It's the point in space where reflected light rays converge or, more to the point, appear to converge. Now I keep saying actually converge versus appear to converge in a careful way because there are actually two kinds of images. There are real images and there are virtual images. Let's talk about the plane mirror for a second. When you look at your image in a plane mirror, your mirror twin appears to be standing inside of the flat surface of the mirror. Now you and I both know that that's not physically possible. There's no way that this three-dimensional reconstruction of ourselves is quite literally inside the surface of this flat 2D plane off of which light is reflecting. And this gets to the heart of what is meant by virtual when you're talking about a mirror image. A virtual mirror image is an image that appears in a place where it physically cannot be, and for the case of a mirror, this is behind the surface of the mirror. Only your eye makes it real. You really think that your mirror twin is on the other side of this flat glass surface, but in reality they're not. It's not possible to place a screen or a camera, for instance, physically inside the surface of the mirror to take in an image of your mirror twin. In order to take an image of yourself in a plane mirror, you have to put the camera outside the surface of the mirror. If you put it behind the mirror, you won't see anything because the mirror blocks light. Now this is to be compared and contrasted to a real image. A real image from a mirror is one that appears on the side of the optical instrument, the mirror in this case, where it could actually be physically located in space. And if you were to put a screen or a camera at that point, you could actually show the image clearly. Real images from mirrors appear to be located on your side of the mirror. You'll see this demonstrated either in the video or in class, but there are images formed by certain kinds of reflective surfaces, certain kinds of mirrors that appear to hover outside of the physical boundaries of the mirror itself on your side of the mirror. So if you put a camera there, you can take a clear, crisp picture of that real image. For lenses, real and virtual images are defined similarly, but there are some subtle differences with mirrors that we'll get to when we talk about thin lenses. So, again, we can revisit the picture of the plane mirror. We have this clay jar and we see the reflection of the clay jar. That reflection appears to be located on the other side of the mirror. And if you were to put a camera behind the mirror, you'd see nothing. This is a virtual image. Your eye makes it real, but it's not really physically located on the other side of the mirror. So, again, driving this home, because this is something where it's very easy to get caught up by what you mean by real, what you mean by virtual, specifically for mirrors now, focusing on mirrors, not generically on optical instruments. For mirrors, real images appear to be located on your side of the mirror. And it's actually possible, as I said, I will show this to you. Virtual images for mirrors are images that appear to be located behind the mirror, sort of inside the mirror world, even though there's no actual world there. It's possible to place a camera or a screen behind the mirror and see the image. We can begin to understand image formation geometrically using a plane mirror by doing something called ray tracing. Ray tracing takes advantage of the geometric properties of light rays. Remember, a light ray is merely an arrow that indicates the direction that wave fronts are traveling from an emitted wave of light. We can characterize the motion of the wave merely by looking along a direction, seeing which way the wave fronts are moving and pointing an arrow in that direction. So, for instance, consider a simple object like this upright dark blue arrow, which I will denote as O, representing the object whose image will form on the other side of the plane mirror. Now, we can see that the image will form there, on the same side of the mirror as the object by doing ray tracing. Ray tracing is merely where we pick a number of representative light rays emanating from a common point on the object. We follow them as they strike the surface of the mirror, reflect according to the law of reflection, and then bounce away from the mirror. We then figure out where those reflected rays converge or appear to converge in space, and that point of convergence will represent the location on the image where the point on the object emitting the rays appears to be reflected. So, let's consider the tippy top of the arrow as our point of emitting light. So, we have light rays going off in all directions from the tippy top of the arrow, and some of these are going to strike the plane mirror. Let's look at a few of them and see what they do, and we'll use the law of reflection at each step. Consider a ray that leaves the top of the blue arrow and heads out parallel to this dark black line I've written and labeled as axis. That ray is following a line that is exactly parallel to a normal to the mirror surface. That is, the axis is at exactly a right angle to the mirror surface by construction in this image, and so when a ray travels along that line and strikes the surface of the mirror, according to the law of reflection, its reflected ray will come out at the same angle on the other side of the normal. But here we're coming in along a normal, so the angle with respect to the normal is zero, and so the angle of reflection will also be zero. And so what we see happens to this ray that comes in parallel to the axis I've drawn here is it strikes the mirror surface and it bounces backward back toward the object, and I've indicated this as an arrow shooting off to the left side of the picture horizontally. Now we could look at another ray, a ray that rather than coming in at zero angle to a normal to the mirror surface, instead makes some angle theta 2 with respect to the normal to the mirror surface. So I've drawn a sort of dot dashed line here and labeled it normal to mirror surface, and I have placed that line perpendicular to the plane mirror surface at the point where the second ray strikes the mirror surface. And we see that comes in at a non-zero angle, and of course the law of reflection tells us that it will be reflected at an equal angle theta 2 on the other side of the normal, and with a nice precision drawing program like that available in Libre office I can go ahead and make these angles exact according to the law of reflection and draw the arrow coming out. We see that rather than coming out parallel to the axis, this one comes out at an angle theta 2 with respect to the axis, and it appears to diverge away from the first ray that reflected off the mirror. Let's look at a third ray. This ray comes off the top of the dark blue arrow and strikes a point on the mirror very close to the floor in this picture. That is very close to the line labeled axis that passes through the mirror itself. That, according to the law of reflection, reflects away at the same angle with respect to the normal that the incident ray came in, and we see that this one diverges even further away from the second and the first ray that were reflected. What we observe is on our side of the mirror according to this geometric picture of optics. We have a situation where the rays do not converge at a point on our side of the mirror. That's okay. No need to panic. All you have to do is think about where in space these rays could have converged, and to do that you can extrapolate them backward. So you can take the reflected rays and you can draw a line that points back along the trajectory of the reflected ray, even passing through the surface of the mirror into the mirror world, which isn't a real world. It appears to be a reflected world that lives inside the mirror, but there is nothing inside the mirror that's unphysical. We see that in the mirror world, on the other side of the mirror, the rays appear to converge at a single point. That point of convergence marks the location of the tippy top of the image of the blue arrow, and I've drawn that here in light blue to indicate that this is the reflection of the dark blue arrow. What you'll notice just by eye is that for a plain mirror, the distance of the object to the surface of the mirror is pretty much equal to the distance of the image to the surface of the mirror, and this sort of confirms using a geometric optical picture what we know from experience, which is that our image in a flat plain mirror appears to be equidistant from the surface of the mirror as we are to the surface of the mirror. And indeed, we see that the image is expected to be upright. It has the same vertical orientation as the object, and it's the same size. You'll note that the horizontal ray passes right at the top of the image, just like it did on the object, marking the top of the image, and those are exactly the same heights. So we have an upright, virtual, and preserved image. It's not magnified in any way. It's neither enlarged nor reduced, and this is exactly what reproduces what we see in the natural world. If we make a plain mirror and we look at our image in it, we see these features, and we see that treating light waves as rays, which indicate the direction of the electromagnetic waves travel, allows us to reproduce that picture that we see in the world around us very quickly. And we didn't even have to pick multiple points on the arrow. We just picked a representative point and found out where that representative point was in the mirror world. As an exercise, why don't you go ahead and pick the bottom of the arrow, where it sort of stands on the ground, labeled axis, that black line here. Why don't you pick that point as the point of emission of rays and see where that... We've explored a few concepts with the simple plain mirror, which is the simplest, specular, reflective surface that we can handle at this point in the discussion. So let me summarize what we've learned by ray tracing a few key beams of light emanating all from a common point in space and then being reflected in a specular way by the surface of a plain mirror. First of all, the image of the plain mirror is virtual. The rays that are reflected off the surface of the mirror appear to converge on the side of the mirror opposite where the object is actually located. That is the thing that's emanating the rays in the first place. Now, magnification. It's possible with different kinds of mirrors to make your image look bigger or smaller or the same size. The ratio of the height of the image to the height of the object, h' over h, is defined as the magnification factor. So for instance, in a plain mirror, you will find a perfectly flat plain mirror that the magnification factor is 1.  Now, this is not the case for other kinds of mirrors.  They can make you look very fat or very thin, very tall or very small. And all you have to do to get those different kinds of images with different magnification factors is to change the reflecting surface's shape. And we'll explore a few very simple variations on the plain mirror in a moment. Let's look at spherical mirrors. A spherical mirror is most easily thought of if you imagine a big, perfect sphere of mirror material. So imagine taking that plain mirror and wrapping it around a basketball so that you had a perfectly reflective mirror surface basketball. That is a sphere. Now, if you were to cut a chunk of that basketball away, it would retain the curvature of the original sphere with the original radius of that sphere, which defines the curvature for that object, and yet it would only be part of it. So you see here in these pictures a few examples of actual spherical reflectors. So for instance, in the right-hand side, we see what appears to be a giant ball whose outer surface is a mirror. In the left big image, the one that's tinted gold or orange, you see a picture of a person taking a photograph of their camera and the room behind them reflected on the surface of a holiday ornament, a Christmas ornament. So this is just a spherical reflector hanging on a Christmas tree, Christmas bulbs. Very common. You can buy them for fairly cheap, and they're a good example of a spherical reflector. They're almost completely a round sphere. They have a little hanger at the top, which distorts the shape a little bit, but they're a pretty good example of a perfectly round reflector. In the top left in the small inset image, you see an example of a spherical mirror that is not bowed out but bowed in. We'll explore the naming conventions for these two kinds of spherical mirrors in a moment, but unlike the other two that are pictured on this slide, which are bowed outward, this mirror bows inward. It's like the inner surface of the sphere was coated in a mirror, and then you sliced off a chunk of the sphere and held it so that it curves away from you. This is a cosmetic mirror.  So whether it's putting on makeup or shaving, these cosmetic mirrors are very useful. They are spherical mirrors. They're shaped as if they were cut out of a much larger spherical ball, but of course they're not huge. They're made on your vanity in your bathroom. And their job is to magnify your face and show you very close-up details so you can do fine work on your face without injuring yourself in some way. So these are all examples of spherical mirrors. Cosmetic mirrors, they bow away from you. Ornaments on a Christmas tree, they bulge out toward you, and they have an outer reflecting surface. And then for instance, this strange structure over here on the right where you see people photographing themselves in it and reflected in it, that's another example of a mirror surface, a spherical mirror that bows out toward you. A mirror that bows in away from you is known as a concave mirror. And you can remember this naming convention because it's like a cave, right? When you're looking into the mirror surface, it's like a hollow, and it's aimed away from you. So you can remember concave mirrors because they're like little caves that you look into to see your reflection. Now this picture illustrates a few key features of any curved reflector. And specifically we're focusing on spherical curved reflectors. There is a point known as the center of curvature. Now if you imagine extending the grey spherical concave reflecting surface I've drawn here, all the way around, so it makes a circle and then extend that into a sphere. The point C, which is the center of curvature, lies dead center in the sphere. It is the location where all radii in the sphere converge. Now this may not be the same as the location where light rays reflected off the surface of the concave mirror will focus. That point where reflected rays will meet is known as the focal point. And specifically this is the point where rays that come in parallel to the long axis that's drawn here. So you see here this long horizontal line. This is known as the optical axis, and it runs dead center through the curve of the mirror on the right hand side. Any ray that enters parallel to the optical axis will be reflected through the focal point.  So to review the terminology for a concave mirror, really for any curved mirror, but focusing on this one for a moment, you have the mirror itself, which may only be part of a sphere. It has a central point around which it is symmetric. The axis that cuts through that symmetric point is known as the optical axis and is drawn here as a horizontal line. There is a point on that line inside the curvature of the mirror that represents the location where all spherical radii meet. That is the center of curvature. So a line drawn from C to the surface of the mirror will always have a length of the radius of the original sphere. And then finally you have the focal point where incident parallel rays, that is parallel to the optical axis, will be focused by the mirror. Now, in a discussion of mirrors, especially as we're going to get into a more complex mirror like the spherical mirror, it's important to define some terminology for rays. And specifically I want to define the concept of principal rays. Now you might think, oh gosh, if I have to ray trace a picture, if I put an object in the last slide and then try to figure out where its reflection might be, I have to trace all these rays. There could be millions of them or billions of them. Well, the good news is that you only have to pick a point on the object and then emanating from that point, you just have to pick a few principal rays that are fairly easy to remember once you get the hang of it. And you just always draw those and they will tell you where the corresponding point on the image is located. So principal rays are just these few special rays that when used together help you to quickly locate a point on an image that is equivalent to the original point where light started on the object. And they're much easier to use than other rays and they're representative enough to pinpoint the image. So for instance, for spherical concave mirrors, we can talk about a parallel ray, which I've already mentioned. A parallel ray enters parallel to the axis through the middle of the sphere, the optical axis. All parallel rays meet at the focus of the spherical mirror. So wherever that point is, f, for a spherical mirror, that's where that ray will pass through. A focal ray is one that enters before striking the surface of the mirror by passing through the focal point. The focal ray will then bounce off parallel to the optical axis. So when a ray that comes in through the focus reflects off the spherical surface of the mirror, it will travel after reflection parallel to the optical axis. And then finally, I haven't written it here, but another really easy one to remember is a ray known as a central ray. A central ray is one that enters through the center of curvature of the mirror, and when it strikes the surface of the mirror, it's reflected directly back along its original path. And you can figure that one out pretty quickly from the law of reflection. We know that if a ray strikes a flat surface along the normal to the surface, it will be reflected back out exactly along the path along which it came. Because the law of reflection says that the entering angle is equal to the exiting angle on the other side of the normal. So if you enter with an angle of zero relative to the normal, you must exit with an angle of zero relative to the normal. So any ray that comes in on a line that's perpendicular to the reflecting surface will go back out along that same line. Since a ray that passes through the center of curvature of a spherical concave mirror is by definition traveling along a radial line, and all radial lines are perpendicular to the surface of the sphere where they touch, the ray that enters by passing through the center of curvature will necessarily be reflected back out along a path that takes it back through the center of curvature. Now if you remember your geometry, you know that you only need to find out where two lines cross in order to locate a point in space. The point of intersection can be determined merely by drawing two. You're welcome to draw all three principal rays, parallel rays, focal rays, and central rays if you choose. You only need two of these in principle to locate a point on an image that corresponds to the point on the object where light originated from. So let's draw as our object a vertical blue arrow shown here and labeled as O for object. It's perfectly straight. It's perpendicular to the optical axis. So this could be a person standing there or it could be a pencil that's being reflected in the mirror or a candle that's standing upright on a table being reflected in a concave spherical mirror. And we can try to figure out where a corresponding point on the image will be located. So for instance, if we imagine rays of light emanating outward from the tip of the arrow, we can follow just a couple of principal rays. We can trace them and we can see where they converge in space or where they appear to converge in space if they don't do so on our side of the mirror. So in this case we have our object located to the left of the center of curvature of the mirror. We can follow a parallel ray, a ray that starts out by being emanated parallel to the optical axis. It travels toward the surface of the mirror. It strikes the mirror and according to the rules I told you a moment ago, it's reflected and it passes through the focal point of the concave mirror. We can also think about an incident focal ray. This is a ray which starts its journey from the tip of the arrow, but it passes not parallel to the axis, crosses through the optical axis through the focal point. It then strikes the surface of the mirror and it bounces off parallel to the optical axis when it leaves and where those two lines converge the incident parallel ray reflected and the incident focal ray reflected locates where the top of the arrow image will be located. We see interestingly that the point of convergence is not above the optical axis which is where the object pointed, but below the optical axis which means that the image formed by this concave mirror putting the object to the left of the center of curvature will be upside down. This is known as an inverted image. It is real because this image appears to form on the side of the mirror where the object is located so that defines it as real. It is inverted because it is upside down. Its orientation is opposite what the orientation of the object was and it is a reduced image. We see that by carefully ray tracing using a computer program we very clearly get an image which is reduced in size compared to the original object. We refer to this as a real inverted reduced image of the original object O. We can look at another case with the same concave mirror. Here we could locate the object between the center of curvature and the focal point. So now let's trace the parallel ray and the focal ray. The parallel ray strikes the surface of the mirror and then passes through the focal point. The focal ray passes through the focal point, strikes the surface of the mirror and comes out parallel to the optical axis. And now we can figure out the reflected rays converge. The reflected rays converge at a point behind where the object was located. It is still inverted, it is still real, but now the image appears to be larger than the original object. So we refer to this as a real inverted enlarged image. This is all determined simply by doing very basic ray tracing. Here's an example of a candle which is our object and a concave spherical mirror as you can see in the background here. The candle is sitting on a table and if we look at where the image of the candle appears to be located, the candle's image appears to be floating outside of the surface of this concave mirror. Notice how the image of the candle appears to bow out whereas we know the surface of the mirror bows inward away from us. Whereas the candle appears to bow outward toward us. It appears to be hovering above the surface of this mirror, weird, right? But this is a real image. You don't get these from plane mirrors, but you can get them from concave spherical mirrors. This candle happens to have been placed exactly at the center of curvature and when you place a candle or an object exactly at the center of curvature, you'll get a real inverted image with the same height as the original object. If we move this candle back a little bit, we'll get a real inverted reduced image and if we move the candle forward a little bit between the focal point and the center of curvature, we'll get a real inverted enlarged image. Now what happens if you move that object deep inside the focal point of the concave mirror? So that's what I've sketched here. We now move our object O inside the focal point. It's now between the surface of the mirror and the focal point of the mirror. We can do our ray tracing again. So now if we send a ray out of the tippy top of the blue arrow, parallel to the optical axis, it doesn't have to travel very far and we know that when it strikes the surface of the mirror, it will be reflected in such a way that it will want to pass through the focal point of the mirror and so I've drawn that here. Now in this case, of course, we know that the object is in the way of that ray and we'll come back to that consequence in a moment. But that ray is going to be blocked by the object, not to worry because what we want to know in order to determine where the image is is where these reflected rays appear to converge in space. Let's look at a focal ray. Well, this is where things get a little difficult but you just have to remember the rule and you'll be okay. A focal ray can be one that passes directly through the focal point and then strikes the mirror surface. We've been looking at those. But in this particular case, it's not possible to send a ray through the focus and have it strike the mirror. There's no mirror back there for it to strike. A focal ray, however, can be one which could have originated from a point at the focal point, then travels in a direction on a line between the focal point and the surface of the mirror, then strikes the mirror and then bounces. So that's what I've drawn here. I have a focal ray which you can trace back to the focal point. It appears to have originated along a line between the surface of the mirror and the focal point. But of course it started its journey on the top of the object. It just appears to project back along that line. It strikes the surface of the mirror and like all other focal rays that we've been looking at so far, it reflects backward parallel to the optical axis. Now you see we have a problem here. It's clear that these two reflected rays do not converge anywhere on the real side of the mirror. So rather, we have to think about where those reflected rays appear to have originated from after they've reflected. And if we trace them backward in space, we find out that they appear to have converged on a point on the opposite side of the mirror. That is, the image of this object will appear to form on the other side of the mirror. It's virtual. We notice it's upright. So it has the same orientation as the original object. We also notice that it's larger than the object. It's enlarged. So when you move inside the focal point of a concave mirror and look at the image that results, what you will find is that light rays appear to originate from the other side of the mirror, even though physically they can't have come from here, that's where they appear to have originated from. And so you get a virtual upright and it turns out enlarged image. No matter where you go past the focal point, you'll get an enlarged image. Well, here's an example of that. The mirror has a little groove in the bottom. This lets you move an object within the focal length of the mirror and that's exactly what has been done with the candle on the table here. What's kind of cool about this is that you can see the difference between images of objects that are behind the focal point and objects that are within the focal point. Look at the room reflected in the mirror. It's still a reduced, inverted, real image. You have the chalkboards, the camera, even the tabletop surface that we can see reflected in the mirror. All of that is clearly outside of the focal point of the mirror. It's all inverted. It all appears to bow outward from the surface of the mirror so it's real. It appears to be on our side of the mirror and it's all inverted and it's all reduced. But the candle, which has been moved inside the focal length of the mirror, it appears now, its image appears to be on the other side of the mirror. Look at how it curves. It curves following the curvature of the concave mirror. It bows with the mirror. The candle is huge. Its image is greatly enlarged over the original object. It's upright. The orientation of the candle's image is now the same as the original candle. We see the flame is magnified and everything. This beautifully illustrates what it means to form images from objects that are beyond the focal point and within the focal point of a concave spherical mirror in one picture. Now, what if we flip that mirror surface around so that it's not bowing away from us but bowing out toward us? This is known as convex. This is a little harder to remember. I find it easier to remember concave because it's like a cave that bows away from me and I have to look into the cave to see my image. Convex bows out toward you and so we can think again about ray tracing. Now, we flip the sphere around so the focal point is on the other side of the mirror and the center of curvature is on the other side of the mirror from where we're putting the object. The object is on the left. The focal point and center of curvature are on the right side of the mirror and so now we can try to send a ray parallel to the optical axis and it will be bounced off of the convex surface of the mirror. It will appear to track back through the focal point so you see I've traced that ray, that reflected ray that came in parallel. It bounces back on the same side of the mirror as the object but it appears to have originated from the focal point on the other side of the mirror. Its trajectory takes it back to that focal point. Similarly, if I send a ray along a line toward the focus on the other side of the mirror, when it strikes the mirror surface well before reaching the focus, it will bounce off parallel to the optical axis and again we see a situation where these rays on our side of the mirror, they don't converge at a point. They're happily traveling away from one another never to meet again. But if we track them back, if we take the reflected rays and we figure out well where did they appear to originate from? We find that they appear to have originated from a point on the other side of the mirror so this will be a virtual image. That image is upright and it's reduced in size compared to the original object. So in fact it turns out that these are the only kinds of images that convex mirrors that is bowing out toward you. Convex spherical mirrors can only ever make virtual upright reduced images. So here's an excellent example of that. Flip that concave reflector around. Now you have a convex reflector and we see that no matter the distance of the object from the mirror all reflections, all images are virtual, upright and reduced. The camera in the picture appears to be much smaller than the camera in reality. The blackboards certainly look far tinier than the actual blackboards. The candle is reduced in size. It's all upright and it all appears to be located on the other side of the mirror surface, virtual. So virtual, upright and reduced. Here's an excellent example of a convex mirror in the wild. You've probably seen these before and never thought about what they were. These are special mirrors placed at dangerous places where you have to leave a driveway or maybe at a sharp corner where there might be a driveway located or where you can't see cars around the corner of a road. Often cities, towns, other municipalities they'll put up these convex reflectors. These are convex spherical mirrors. So they look like pieces of a larger spherical mirror that have been cut to size. They bow outward toward you. They're highly reflective on the outside. And what they do is they show you images of objects that may not be visible to you where you're sitting, but light rays can reflect off at extreme angles from objects outside your immediate field of vision and be made visible to you. The danger of this though is that all of these images appear to thankfully they're upright and they're virtual but they appear to be smaller than they actually are. You have to be very careful with mirrors like this because you may misjudge distances and sizes as a result of the fact that you have a reduced image in the mirror. You can't really judge well distances looking in this mirror. Cars may in fact actually be closer than they appear. Objects traveling toward you may be larger than they appear in the mirror and so you may misjudge the danger. You have to be very careful when using these mirrors but nonetheless it's better than not being able to see the corner at all. So you'll often find these at driveways and other dangerous places where visibility may be compromised and drivers need to see objects that are not in their immediate field of vision. We can employ something called the mirror equation. It's based on the geometric principles. In fact that's where it's derived from. But it's a nice compact simple equation that you can whip out given information about an object or an image or a mirror, for instance, its radius of curvature or its focal length things like that and you can actually solve numerically questions of image formation object distances and so forth. The mirror equation is very simple. Keeping the conventions in mind is something that you'll have to practice but the equation itself is fairly straightforward. If we denote the distance of the object from the surface of the mirror, specifically from the point where the mirror touches the optical axis as a distance p and we denote the object that the image forms from the point of contact with the optical axis and the mirror denote that as i we can relate the focal length of the mirror which is fixed by the geometry of the mirror to the object in image distances using this mirror equation. 1 over p plus 1 over i equals 1 over f that is 1 over the distance to the object plus 1 over the distance to the image equals 1 over the focal length of the mirror. Now, as I said the distance p is the distance of the object from the point of contact with the optical axis which is the mirror center for the spherical mirrors we've been considering. This is by definition a positive number. Object distances are positive. The side of the mirror on which the object is located defines the location of all positive distances. So your coordinate system for optics problems is defined not by positive increasing numbers on an x-axis and negative decreasing numbers on an x-axis but rather positive numbers defined by whether or not those distances occur on the same side of the mirror as the object negative distances occur on the side of the mirror opposite where the object is located. The distance of the image from the mirror center is written as i. This can be a positive number. If it's positive it means you have a real image. Or it can be a negative number in which case you have a virtual image. Real images form on the same side as the object. Virtual ones form on the opposite side of the mirror from the object. So an image will have a negative image distance if it forms on the opposite side of the mirror inside the mirror world where it physically can't be located. And it will have a positive distance if it forms on the same side of the mirror as where the object is located. I find it helpful to keep a little table of information like this in my notes so that as I'm working problems I can refer to it and check my answers and make sure that everything makes sense. The radius of the mirror is written as f. It is designed into the construction of the mirror and in fact for a spherical mirror the focal point of the mirror is one half of the radius of curvature of the mirror. So the radius of curvature, remember, is the radius of the sphere from which the spherical mirror was cut effectively to make the spherical mirror you're looking at.  So for a spherical mirror the focal length is related directly to the geometry of the sphere from which the mirror might have been cut and the focal length is one half of the curvature. This will come in handy in case you ever need to solve for the focal length given the geometric properties of the mirror itself. Now the reality or virtuality of an image is determined by the sign positive or negative of the distance i. You can also determine things like the magnification factor and whether or not the image is upright or inverted when it is produced by the mirror. Magnification is a simple equation the magnitude of the magnification factor is merely given by the ratios of the height of the image and the height of the object. So if you have an object that's one meter tall and you have an image that's two meters tall the magnification factor is two. If you have an object which is one meter tall and an image that is one half meter tall then the magnification is one half. One means there's no magnification. A number greater than one means there has been an increase in the size of the image relative to the object and you get positive magnification. You get enlarged images as a result. If you have a magnification factor that's less than one you get a reduced image. So it's an image smaller than the original object that it is a reflection of. For spherical mirrors using geometry we can derive we're not going to do that here but we can derive a very nice relationship between the magnification factor and the image and object distances. So m now not absolute value of m but m itself which can be a signed quantity is equal to negative i over p. So for instance magnification can be negative. What does that mean? What if you get a magnification factor of negative one half? Well all that means is if i is a positive number and the image forms on the same side of the object you get an inverted image. That's all that means a negative magnification factor gives you an inverted image. So by calculating m you can figure out right away whether or not you're dealing with an inverted image. So if you want to know if the image is real or virtual look at the sign of i, the image distance. If the image is real, negative is virtual. If you want to know if the image is enlarged or reduced in size compared to the object look at the magnitude of the magnification factor. That is equal to h prime over h. That is also equal to the magnitude of negative i over p. That number greater than one means enlarged less than one means reduced and one means the same size. Finally if you want to know if you have an upright or an inverted image look at the sign of the magnification. If it's positive you have an upright image and if it's negative it means you have an inverted image. All this information can be determined from quantities that go into the mirror equation. Finally let me close with some tricks of the trade regarding mirrors. It boils down to these sign conventions that I've been mentioning. Objects are at a positive distance p from the center of the mirror. Period. End of sentence. There are no negative object distances for the problems we're going to be dealing with. Images can form either on the same side as the object in which case i will be greater than zero and you have a real image or they can form on the opposite side of the mirror from the object in which case i will be a negative number less than zero and that means a virtual image. Focal points for mirrors can be on the same side as the object such as in concave spherical mirrors there the focal point is on the same sign of the object. In that case F is a positive number. So for concave mirrors the focal length is a positive number but if the focal point is on the opposite side of the mirror from where the object is located then you have a negative focal length and convex mirrors have negative focal lengths. Finally magnifications can be positive numbers meaning that you have an upright image that is formed or negative numbers meaning that you have an inverted image that has formed. So here are the helpful sign conventions that will aid you in wading through mathematical problems involving mirrors, images and all the details of the formation of those images. This concludes the lecture on mirrors. In the next lecture we will move into thin lenses so rather than looking at the effects of reflection on rays and ray tracing we will look at the effects of refraction on rays and ray tracing we will develop a very simple lens system known as the thin lens and we will look at the implications of image formation for different kinds of thin lenses.


Okay. I just come out of confession, right? Right. But it just doesn't work for me. I mean, if I do something wrong, I just want to pay for it my way. So I do my own penance for my own sins. What do you say, huh? That's a clip from a very old Martin Scorsese movie, Mean Streets. It's Harvey Cattel there. And Scorsese is going to come up a couple of times in this introduction to my interview with the excellent Miguel Connor. This is kind of part two of an interview we did just a few weeks ago. And in this part two, I pulled Miguel back into my ongoing fascination with the conspiracy surrounding the origins of Christianity. So without getting too far into the weeds, which I don't think we can avoid getting too far into the weeds on this topic, Martin Scorsese has always been fascinating to me. He's obviously an incredible filmmaker, but he's also someone who is playing out in his art, the larger Christian drama, the questions of good and evil, the questions of what are we supposed to do with our lives and our sins and all the rest of that. But he's not only playing it out in this artistic, metaphorical archetype kind of way. He's also a practicing Catholic. He's meeting with the Pope and he buys into that stuff. I mean, here's a clip from an interview he gave about his faith and in particular his faith as a Catholic. I think it's the depth of faith. It's where one it's the struggle for the very essence of faith. The vehicle that one takes towards faith can be very helpful as a church, the institution of the church, the sacraments. Yeah, I'm kind of with right up to the end there, right up to the vehicle part. What if the vehicle Christianity, Catholicism, Judaism, the Bible? What if that vehicle isn't what you've been told it is? What if the real vehicle sounds more like this?  And even though Scorsese didn't have a microphone on that conversation, I would suggest he came pretty close in his movie, The Irishman. And in particular in this clip, where the modern day instantiation of the cult of Mithras, that being the Italian mafia, are plotting the assassination of Caesar.  Remember this clip?  Doug Jimmy, I'm sorry for his troubles. The old time he spoke to the old man, the old man taught this on Jack.   So maybe I'm right about the Josephus slash Vespasian Psiop. I think I make a pretty good case, but maybe I'm right. Maybe I'm wrong. The real point is that it matters. It matters in some fundamental way. If we're going to talk about this here and now reality. I mean, on another level, as our excellent guest, Miguel Conner brings us back to at the end. Fundamentally, it doesn't matter, but it does matter. Listen to this show, but it doesn't matter. Listen to this clip. The game doesn't change. The most important thing is you're waking up and your inner flame or soul or consciousness. That's the most I tell people, it doesn't matter if you walk out today and you see Bigfoot or you see an alien ship land or you find out that the Rockefellers are still worshipping Mithras and ruling are the United States government. Your job is still the same, which is to wake up and find out where your purpose is and move there. Because the other things, in a way, it's fun, but compared to infinity to, as you say, extended consciousness and all that, it's a drop in the bucket. You know, don't lose sight of the big game, which is who you are, which is just an amazing individual that has purpose and meaning in this world. Stick around for my interview with Miguel Conner. And please, I'll put out the plea again. Share this show. I think this is such an interesting thing that we're working on. I want to work on it together. I want to hear from other people in this community who can either punch holes in this theory or add support to it in some way. Share this interview with anyone you think would be interested in hearing it. I have a bunch of new ways of sharing and interacting on the skeptical website. Go there and check it out. And please join me in this fun, fun, fun discussion. Here's my interview with Miguel Conner. Nice. Okay. And I say that Miguel, because I want to pivot a little bit. And I might even break this into two parts, because I am talking to Miguel Conner from Anne Byte Nostocrity. And we just had a great chat about his new book, Ten Snackable Meditations. And now I want to pull him in a totally different direction. I felt like I needed to pause. Miguel is one of my go-to people for these kind of book projects. I feel compelled, even if no one reads them. You know, no one reads books. So I don't know how you're going to do with your book. But I think this is really, really such an interesting topic for me. And it's right up Miguel's alley. So this is going to be a little bit inside baseball. If you like that, then you're going to might enjoy it. If you don't, then you might not. So Miguel, I did kind of tip my hand here a little bit in terms of what I wanted to talk to you about. But I've been seeing it almost as a Caesars Messiah 2.0. I love Joe Atwell. And I just have a lot of respect for him. He's been on the show, even though he's not responding to my emails right now, because maybe the last time I had him on, I hit him too hard with the ET thing. And not everyone is not everyone is as open as you are. Like I said, you can throw you in the middle of the pool and you swim to the side. I'm going to jump right into a really important quote that I think is the springboard for this whole discussion. And again, folks, inside baseball here, so I don't feel a need to kind of bring everybody up to speed. The point is, what is the origin, the true origin of Christianity and is Christianity best understood first as a conspiracy theory, as a PSIOP, as an operation, a way to control the population, which the Romans were so, so adept at. Is that the first way that we should consider it? That doesn't mean that you can't have a personal spiritual relationship with Christ consciousness. I mean, one, no one can tell you you can't. You don't need me to give you the permission. But number two, I'm convinced by the evidence that that is in whatever respect we want to call genuine. That is genuine. That's real. I don't know how that works, but it certainly seems to be true that you can have a genuine personal spiritual relationship with Jesus that is completely separate from this. And when I say this, I mean none other than the writings of Josephus and the quick history reminder. Josephus is the primary source we have for this history.  In some respects, he's obviously biased in all these ways. But then they say, well, gee, I know we lost our keys out in the parking lot. But the light is so much better over here under the street lamp. Can't we look over here? Well, no, you can't if he's discredited. But here's what he wrote in War of the Jews. And I would suggest deep inside baseball now. This is the first Syop. This is the one that Joe from Caesar's Messiah missed. He missed this. He he's aware of it, but he doesn't point out the significance of it. Josephus writes to his brethren. But what more than all else incited them to war that has incited the Jews to rebel because this is again, this is Josephus writing as he has joined Vespasian. So some people consider that a turncoat.  Do you want the million dollars or do you want to live till tomorrow?  So he is then turns to writing to his audience, the Jews. And he from the beginning says, I am the super Jew. I know more about I'm a better Jew than anyone else because I've studied more. The other thing he says in this writing is I'm going to tell you the truth, not like these other historians out there. I'm going to tell you the truth. Those are Josephus's own words and were the Jews back to the thing. But what more than all else incited them to war was an ambiguous oracle, likewise found in their sacred scriptures to the effect that at the time, one from their country would become ruler of the world. Ha, Messiah, the Messiah. This they understood would mean someone of their own race. And many of the wise men went astray in their interpretation of it. All those Jewish elders at the temple, they went astray. Josephus is telling the general population in Judea. The oracle, however, in reality, signified the sovereignty of Vespasian. Vespasian is emperor. He's Caesar, right? Think Caesar. He's the new Caesar. He's the new guy in town who was proclaimed emperor on Jewish soil. So what he's saying is, hey, you know what? You missed this little trick in there when our our Jewish faith, all our books said that the Messiah would be a Jew, of course. They just they just missed it a little bit. What they really meant is that would come from Jewish soil. And this guy, Vespasian, he landed here. Of course, he landed here to slaughter all of us. But he was on Jewish soil when it all happened. My point is this cannot be understood to me as anything other than a Cyop. There can't be anything authentic about this. What do you think? Oh, yeah, there's no doubt about that. I mean, I guess I should quote Philip K. Dick's famous dictum, The Empire Never Ended. Even if you don't take it literally, the Romans really created the ultimate, you might say, system for control. And they had complete control over everything. I mean, for example, magic, the Romans over regulated magic to the point that it just didn't work and they had their hands. They knew magic could be dangerous in the hands of a population. You had to be like in the outside. So there was nothing. The Romans had control over everything. And this sort of template has been borrowed by empire after empire. And the scholars, but even before Joatt, well, scholars always said, it's so obvious that Luke, the Gospel of Luke, borrows heavily from Josephus that acts of the apostles again. It's all Josephus, whoever. Luke is just borrowing things and putting it with Josephus. So but the question has to be is, well, there's no doubt that the Roman fingers are on Christianity because the Romans were smart. They knew they had to control. There's evidence of them controlling other religions. There were the question is really when and at what time. I mean, for example, we quoted Augustine in our first half, Alex, and Augustine famously said Christianity has always existed since the beginning of time. So what is what is Augustine talking about? Well, he's kind of hedging his bets or stretching things. In other words, the idea of this mystery cult of a rising dying Godman, whether it's Addis or Osiris or some of the many other dying and rising, signifying signifying the renewal of the land, the renewal of your soul, the rebirth, all that had always existed throughout before the Roman Empire, before the Greeks. And that was going around. And Christianity was, you might say, the Jewish manifestation of this mystery cult, the rising and dying Godmen. We're getting into Echeria s sort of domains and at will. And Echeria agreed on a lot of things, but disagreed on a lot of things. So when did this cult come in? And when did the Romans say, what's the name of the guys who did that book? James Aliphante. I mean, and Warren, Warren, I forget the name of it, but they put out the book a couple of years ago where they even bring archaeological evidence that the Vespasians were creating or infiltrating Christianity because their their their seals and everything were used by Christianity before even the Jewish war. But they think that Paul was probably not part of this, that there was also another that part of Christianity was still offering this mystery cult and hadn't been completely infected by the Roman powers. And Joe Atwell himself says that the Gnostics were an answer to the Roman corruption of Christianity because their writings are so full of parody. They're making fun of the Jewish orthodoxy. They're making fun of the Roman government. They're they're very in a very subtle way. They're mocking what Christianity had become in the power of the Roman Empire. So it's a matter of when it happened. I mean, my issue is that people always assume that when Christianity came out, you had the four Gospels, John, Mark, Luke and Matthew. But that's very far from the truth. I mean, you had Marcion in the second century saying, we need a Bible. We need a coded document, a teaching document for this religion. And Marcion went with his idea of the letters of Paul, a few and Luke and his his version of the Gospel of Luke. Marcion also believed we should abandon Judaism and Christianity should be completely like a new religion. And there's two gods. There's a God above God and then there's the Jewish God. And of course, that pissed off the early church in the middle of the second century. But the point is we didn't most of Christianity didn't have this idea of four Gospels. Now, you have to go to Irenaeus around 180 AD. He says, all right, we're going to get some Gospels and I am picking four Gospels and they don't have names. I'm going to give them names. John, Matthew, Luke and John, Matthew, Luke and Paul and Paul. John, Matthew, Mark and Luke. And I'm going to give them names.  You know, Marcus Aurelius' son, he's in the pocket of the Roman power. So you're already seeing there in the power. So the question of what I'm trying to say with this long winded discussion is, yes, the Romans got a hold of Christianity. The question is, when and how much did they get it? Because again, the idea that there was four Gospels is a second century idea. See, I don't think that's really the question. I because and I think that's what that quote that I just offered from Josephus, it pulls us in a different direction. Let me play for you a clip from a very excellent historian, Adrian Goldsworthy, who I interviewed on the show. And this will kind of lead us into a related discussion, but a little bit different discussion as well. If you write about, you know, I've written about Caesar, I've written about Antonin Cleopatra, Alexander the Great. You'll never quite know what someone else was thinking when they do something. The danger is that you create an image of what you think Caesar was like or Cleopatra was like. And then when you come to a gap in the source, you fill it in with, well, this is what my Caesar would have done. So that's a great one to start with.  A couple more I want to play from you from there. Here's what I think we're doing with this. We know how the game ends. We know that Christianity comes to dominate the world on every level, not just on a spiritual level, but on an economic level, on a human suffering level. All these ways, we know how the game ends. So we're always crippled by that and putting the pieces together. What I read in Josephus there is these guys weren't that smart. I mean, if you look at what a half-assed attempt this was to run a Cyop, it didn't work. I mean, the second century, they rose up again. Middle of the second, they rose up again and Hadrian had to destroy Israel. And Christianity was not even a big player till the third, fourth century. It was sort of under the Alamos. Let's process that a little bit differently, because the way that I'd say is if you look at this and you go, what kind of harebrained scheme is this? You you think the CIA screws up a lot, Alex. Exactly. You know, they have money. They screw up all the time. To me, that's just making the point. You know, you don't have to be good. It's the kind of throw it against the wall and see what sticks kind of thing. And that's how this looks to me.    Well, maybe they were tough, but they weren't any more tough than five of the other provinces you're fighting against. That just is written up because that becomes the story. Judaism, here's the here's the truth bomb.  The only reason it is dragged through history is because Roman Cyop number two, which we can't assume they imagined would be as nearly as effective as it was. But it really took off and they got the pieces fell in place and they coopted this rising new thing called Christianity. They didn't even care what it is. And hey, you need another you need the villain in there. Well, the Jews, yeah, we washed our hands of it.  I don't know why we didn't like the Jews, but I just had a sense as a kid, we didn't like them because they killed Jesus kind of thing. We've dragged that for two thousand years. But the point is, when you look at this original Cyop, you see some of the things that you're saying is that, of course, this was a silly Cyop. It had no business working. You know what? The second one, the Christian Cyop was just as silly. It had no business working, but it did work. But let's be mindful of what Adrian Goldsworthy is saying and not look back on the whole thing and try to put all the pieces together as if to say, well, Judaism, what a wonderful tradition with the thunder god and follow all these rules and spin around three times. And it's just it's just more of the silliness and what Christianity emerged out of that is completely designed to control the population. As we saw Constantine, can you get a less authentic spiritual player than Constantine? He certainly wasn't Christian, whatever the hell he was. So that's the level of deconstruction I want to do on this thing. And I know I've laid a lot on the table, but you can kind of see where I'm kind of pushing back on the the narrative that we've been conditioned to kind of buy into. Yeah, yeah, for sure. Again, you have to look at everything as I'm learning everything you thought you knew is false, everything you learned right after is false. I mean, it just it continuously goes. And I should add to this, I think to the Romans, it was important because the the second temple was a huge cash cow. It was one of the biggest buildings in the world. They were they were making a ton of money from taxes.  Let's get rid of it. Yeah, for your listeners, watch that movie Air America with Tom Cruise, which kind of shows you what CIA does. They just throw money. They have so much money. The Romans were doing that with the experiment. So it's a question of why Christianity, if some have said an exclusive religion was probably better to work with things. Some have said the cult of Mithras was becoming so it was much more popular than Christianity. But the problem with the cult of Mithras is that it was a Roman soldier religion, it was very popular, and it had Persian origins.  So we need a bulwark. We need something to counter it. So we're going to create this God or this religion that's pretty much very similar to Mithras, you know, the the host and the sitting down and the formalities and all that. So that's another idea that definitely has to be explored of why Christianity became what it is, because like you said, it was again, Hadrian had to destroy Israel because the Syop didn't work with the Jews. Christianity was just a small religion that Romans and Greeks and others scoffed at until the third, fourth century. And how it became true. And in fact, even then, the idea of Christianity being this world player is kind of false, Alex. You've had Diana Pasulka on your show, and she's actually her first job beside being one of the leading authorities on ufology was a Catholic scholar. And she said that the Roman Catholic Church that we know didn't really happen until the 12th, 13th century. It was a very loose, relaxed people went to church maybe once a month. The church didn't have as much power. The pope wasn't even in Rome. He was in France. It was only until the inquisition and the crusades that Rome, that the Catholic Church became this sort of corporation that we know about world dominating and all that. And before that, you had it was loose. You had the Byzantine Empire, which had his thing. You had all these different sex going on and eliminating each other and vying for money. So even our idea of this holy church popping up and ruling the world and killing witches and all that, that's that didn't happen until the Middle Ages. So it's interesting how, yeah, how we learn these things. Let me throw a couple other clips on the table. So the point that you're making there is something that me and David Matheson talked a lot about, and that is the the Mithris cult, the Mithrin cult. And I think it's best understood. And David certainly agrees with this as a secret society rather than than a cult or religion.  And I think it's been copied over and over and over again throughout history. These guys, you know, when Vespasian takes power, becomes Caesar, they had gone through a period of a year where they had assassinated four different emperors, so they'd come in and the secret society would get together and say, nah, don't like them so much. Boom, he's gone. Next one's gone. And they were the ones ruling.   Doug Jimmy, I'm sorry for his troubles. The old time I spoke to the old man.   Let me jump in here for just a minute and explain something because I think I kind of threw Miguel off a little bit with that clip.  That's a clip from the Irishman and that's Joe Pashie and Robert De Niro. And to me, this is like listening into the cult of Mithras. This is listening into these guys who got together who really ran the secret society that brought about the phony Christianity that we have. So I kind of explained that a little bit to Miguel. And then I pivoted over to a clip from David Matheson and the interview we did about all this good old Roman siob stuff. Here we are talking about the Dead Sea Scrolls and in particular the copper scroll. It was all rolled up on copper and so all of these scrolls are found. The Dead Sea Scrolls found in the 1940s, fragments of over 900 texts, manuscripts and in thousands of pieces like jigsaw puzzles discovered in the 1940s and then given into the hands of an international group of scholars who kept the Dead Sea Scrolls basically under wraps for their entire lives. They didn't let anyone see anything. But there's one scroll known as the copper, the copper scroll. And you see it on the right hand side of your screen. It looks very different than the written scroll. The copper scroll, it was it was all rolled up on copper and so old that they had to cut it in part. And so that's why these pieces now look kind of like like a half of a tube. What is the copper scroll? It's basically the list of treasure. This is how it reads. This is the first words of the copper scroll, not the part that I'm showing. By the way, that's like piece number 18. But on piece one, it says in the ruin that's in the Valley of Acor under the steps with the entrance at the east. So you go to the ruins, find the entrance that's on the east. Then under the steps, a distance of 40 cubits, a strong box of silver and its vessels with a weight of 17 talents, which, by the way, a talent at that time, New Testament talent or that period talent, 129 pounds. So that's 129 pounds of silver times 17. That's a lot. OK, so still, still some more. I got to throw on the table since I have Miguel here. But you see where I'm going with this. The first clip, the reason I played the long Joe Pesci clip is that's what's happening in Rome. That's the meeting of the Mithras cult. That's how they talk.  We're going to do this.  What Matheson is adding, which I think is. And this is the contrast to what you were talking about, right? Is the spiritual? When did Christianity come? And what about Augustus? What? Hey, I'm down for all that. But first, don't we need to understand the more materialistic, archaeological kind of history and the human history of what we did? Here's another interview that just shook my world. I'll pull it up on the screen. And it's a guy named David Brody, and he wrote a book called America. And what he found was all this archaeological evidence of the Romans being in America in the second century. But the connection to it is much, much more interesting because what he says is in that second sacking of the temple. What he suspects happened is that the Roman the ninth legion of Rome, which is this mysterious legion that disappears, you know, they just kind of disappear from history. Well, they were in, if you know anything about Rome, they have these legions and they kind of go off to these far parts of the empire and they kind of never come back. The ninth legion is in Britannia for like 40 years and they're all married up with all the Welsh girls and all that stuff. They have never been to and suddenly get the orders and saying, hey, buddy, need you back in Judea. You guys didn't do it the first time. We're going to do it.  I kind of know where there might be some treasure. And he goes, yeah, but what's going to happen to you? You give me the treasure. You're going to get killed, right? He goes, that's what I was thinking. Maybe I come along with you on the boat, you know? And that's what he finds. That's what the archaeological evidence says. They not only find all these Roman coins. David Brodie does in his book America, but he also finds where they've built in the big Midori in the in the earth and all these other Jewish religious symbols in second century America. So here's the here's the upshot to that. And then I'm going to get back to it. I want to lay the whole thing on you. I got to give you the whole picture to get your to get your full answer. Back to Adrian Goldsworthy, let me throw out one pet theory. Just indulge me, it'll be short, but it has kind of emerged from a couple of different guests that I've talked to. So Josephus kind of famously says, Hey, and I have a revelation. You're going to be, you know, Caesar and the in the copper scrolls, the Dead Sea Scrolls, the copper scroll is a treasure map. And at the bottom of the treasure map, it says, and this is a copy. Josephus being Josephus, super elite among the Jewish elite. What if he knows basically the idea what's in the information contained in that copper scroll? What if he has the treasure map in his head? And what if that is his real bargaining chip with Vespasian? Because it is interesting, isn't it? That Vespasian, who is the soldier, soldier, but really, you know, in unique ways, isn't in line to be the emperor doesn't have the bloodline, doesn't, you know, it has kind of been cast out by Nero. Something happens and now he goes down to Egypt and he seems to have a lot of dough to assemble an army and he shows up in Rome and everyone's like, Oh, OK, I guess you're the guy. How far off is that? Do we have anything that would directly contradict that idea? I mean, the thing is, you've got to remember the timing. So this is 67, Nero still alive until a few months later, where all the bad decisions of the craziness he's done. And I've just been to the British Museum. I could listen to Adrian Goldsworthy for a long time, but it's probably a little bit too much for the show.  Just like the ninth Roman legion did 60 years later, how many years later that is. It's just it's it's just human nature. This is how things get done. This is how Joe Pesci and Bobby De Niro would have done it. What do you think? I've laid a leg, but this is Caesar's Messiah 2.0. This changes it substantially. It's not about a grand conspiracy. They were not that smart. They were just doing the next best thing like you're saying. Just the next thing. Oh, well, what what might work? Well, throw this thing out there that the whole Jewish religion is worth Vespasian is the Messiah. Oh, that didn't work. OK, throw this next thing out there. Let's see if that works. Yeah, government propaganda. Let's try different things. We see it today. We see it throughout history. So it makes sense. And yes, I've also read. Yeah, they have found Roman coins. And I think Brazil or Northern South America. So yeah, this all makes sense perfectly. And like I said, I like where you're going with this because this shows how governments work, how the mind control works.   It's think tanks. It's people being greedy, wanting to retire first. The different Roman soldiers simply wanted to make money to bring back to their family. And that's always important in any situation. So as I say, it's complicated. And I would agree with you, too, that Mithras or I'm going to state Mithras really is the overarching God of Western civilization. He really rules our days today and from skull and bones to so many secret societies. And he keeps popping up even in the Persian times. And it's a sidetrack. But if someone said the people like Cyrus and all those, they probably were secretly worshiping Mithras because this is the kind of God that gets things done because they would sacrifice animals. And Zoroaster very much said, you do not sacrifice animals under the religion of the Persians. But you see these hints going on and this Mithra keeps popping up here and there. And so again, you wonder if there was this parallel competition later on with Mithras and Christianity. But I think in a way Mithras continued to be the ruling God of Western society. I guess the big question, Miguel, that I'd love you to dive into is how are we to understand our here and now history back to the beginning of this interview, this reaction that we all have to what we see going on in our day, just like people have seen and reacted to throughout history, they had their own thing. How do we balance that with this extended consciousness relationship that we have with gods, with spirits, with other entities? Because I think that's so much what your book is all about and your work is all about. And we have to serve both. So how do we do that? Well, as I tell people, the game doesn't change. The most important thing is you're waking up and your inner flame or soul or consciousness. That's the most I tell people it doesn't matter if you walk out today and you see Bigfoot or you see an alien ship land or you find out that the Rockefellers are still worshiping Mithras and ruling are the United States government. Your job is still the same, which is to wake up and find out what your purpose is and move there because these things are fun, Alex. But, you know, for example, JFK, it's so obvious it's tedious when the James Corbett or Corbett say conspiracy is just history plus time. There's so much time with JFK that I can't believe anybody is still holding on to the notion of the single shooter or whatever the hell. But you're still going to have yearly conferences with JFK people going in arguing and debating and paper. That's going to go on for generations. So you might as well not, you might as well continue going down the path like you from Caesar's Messiah 1.0 to 2.0 or finding out Mithras or all this stuff, all this journey that we're in. But the game hasn't changed. You need to keep waking up and you need to be as good as you can and be there for others, the least of our brothers, as I talk about an AMBide. And the answers will come. But the other things, in a way, it's fun. But compared to infinity to, as you say, extended consciousness and all that, it's a drop in the bucket. You know, don't lose sight of the big game, which is who you are, which is just an amazing individual that has purpose and meaning in this world. Can't can't can't top that. Unbelievable. So tell folks as we wrap it up, what's going on with you in the in the AMBide world? Oh, lots of stuff going on. I keep putting out the shows with some amazing guests and my my intros. I keep trying to level it up. For example, in a show, I don't know if it'll be out. Did you know that there was a serial killer that got made into a Buddha? Anguilimala.  But to me, it's like this is a new dimension to go explore. How did the Theravada Buddhas make a serial killer into a Buddha? How does a serial killer become a Buddha? So this is so fascinating things that really say more about ourselves and we can explore parts of ourselves and our relationship to things. And I'm trying to work on sort of a book about I've written so many articles on Gnosticism and all that. I'm trying to do a compilation book hopefully by the end of the year. I want to have like a good intro course on Gnosticism, an online one so people can get the real dope and none of that new age stuff that is out there. So yeah, just doing a lot of voice over work. I'm doing a lot of audio books and commercials to be able to set a career on that one. So if any of your listeners need voiceover, I am your man. I'll get you as I like to say stellar results with down-to-earth professionalism. That's my tag. That's a tagline. I just whip out, you know. So awesome. So that's it. Keeping busy. You auto, we need, we always need more Miguel Conner. So never enough. Awesome having you on. Thanks again for joining me. Thanks for having me. Fun as always, Alex. Thanks again to Miguel Conner and thank you for sticking around for part two of this interview. The one question I tee up from this interview is, what do you make of the cult of Mithras secret society? Is that what it is? I mean, it can be that and a religion and a cult. It can be all those things. But is it a secret society that is probably running these kind of psyops, the same ones we see today, but maybe the same ones that happen back then? That's of course the big question, but I'd love to hear your answers to it. Again, let me know what you think. Engage, connect, share, and stay with me. Have some great shows coming up. Until next time, take care. Bye for now.


Good morning, everyone. So today I want to go over what my diet looks like over the course of a given day. Now it is skewed a little bit right now because I'm getting ready for competition. Men's physique, all natural as always, what I tested and that's gonna be May 12th. Now, I will go ahead and go through my diet and everything that I'm eating and the supplements that I'm taking over the course of the day. But I'm not gonna get too specific in exactly what measurements I'm doing in each or exactly what supplements and when necessarily. Because a lot of it has to do with the plan that was given to me by my coach who's helping me train for this competition and I think it would be unfair and disrespectful to give away everything that he's worked so hard to formulate for me. So I'll give you the general idea of exactly what I'm doing without necessarily the specific details. So here we go. So my first thing I do when I wake up in the morning is I'll have some apple cider vinegar right here, and I'll dilute it in some water, and I'll just drink that on an empty stomach. All right, so I finished 20 minutes of fasted cardio, and then this is what I'm having for breakfast. All right, so for breakfast, I'm preparing a little shake here. So I've got some Omega-3 cage-free eggs. I'm gonna add some coconut milk. Unsweetened. I've got a green supplement for vitamins, minerals, phytochemicals, and probiotics, prebiotics.  And so with breakfast, I'm having, I got my Omega-3 fish oil, a little vitamin D that my coach wants me on, and this natural herbal testosterone booster estrogen reducer, also helping with my competition prep. All right, now it's lunchtime. Normally I after breakfast, I'll go to the gym, work out, and then I'll have a post-workout snack, and then two, three hours later I'll have lunch, but today I had a bunch of like appointments and different things going on. So I ended up having to eat lunch first, and then I'm gonna hit the gym, do leg day-to-day, and then have my post-workout snack. So this is what I'm having. So we got here chicken, broccoli, jasmine rice. That's it. And again, some Himalayan salt sprinkled over top. I love me some Tapatio to flavor it up, give it some spice, and then my aminos. I'm drinking, usually again, I'll have some leftover after my workout. But since I haven't done that yet, I'm just gonna go ahead and drink some with my lunch. And then I have here my Genvoia, that's my HIV medication. I take once a day, and then this little guy is finasteride, which is a generic propitia for my hair, so I can make sure I don't have hair loss. So that's that. All right, so I'm getting ready to head to the gym, and before I start I'm gonna drink this pre-workout, and then I'll be ready to go for leg day. All right, so I just finished leg day, and so within that 30-minute window right after the workout, immediately I'm gonna get my protein on. It's crucial because that's the point when your body most efficiently and readily will use the protein for a protein muscle synthesis, which is what we want.   All right, so I am home now, and as you can see here, I've got my banana to rice cakes, and then I'm gonna take a little post-workout formula here that helps with recovery as well. And that's that. That's my snack.  Okay, so this is, that's my roommate, Lisa, but she doesn't want to appear, but she's gonna appear in here. Okay, okay, okay. So, and this is Raleigh. She's very jealous because she wants my food right now. Say hi, Raleigh. Good girl. Okay. Last meal of the day, beef, broccoli, and jasmine rice. And there you have it. That's it. Ooh, I almost forgot. In addition to dinner, at the same time, I will take my multivitamin and a second dose of my fish oil capsules. Multivitamin and fish oil. All right guys, so this is it. Last but not least, we've got apple cider vinegar, which I'm gonna dive in with water, and then I will take my ZMA pills, which is zinc and magnesium. The reason why I don't take that with my multivitamin is because zinc and magnesium conflicts with some of the things in a multivitamin, and it won't allow your body to absorb all of those nutrients, which is what we want, so we take it at the right time, right? All right, so this is it. Opside vinegar. Mix that baby with some water so it's not too harsh on the tummy, and then these are my ZMA pills. That's it guys. So, you know, I really wanted to do this because I felt that so many people were hitting me up. First of all, wanting to know what I eat and what supplements I'm taking. Normally on a given day. Again, this is a little different because I'm getting ready for competition in about six, seven weeks. But you get the idea of what I'm, what I take, and I'll do another vlog where I go over everything that I would eat. Like outside of competition time and when I'm taking supplement-wise then, but this is what I'm doing now and it also serves to underscore the fact that yes, I have HIV, but I can take a lot of stuff. I can take literally everything that any other natural bodybuilder wants to take. I've run these by my doctor. He's okayed them. I've been taking a lot of this stuff for years at a time. I don't cycle it. It's just every day. That's what I do. It's part of my regimen and I get my routine blood work every three to six months and everything's looking good. Everything's healthy, my liver, my kidney. I can give you advice personally over a physician or someone who's trained in the field because obviously this is just my experience. I'm just speaking anecdotally. So, but the point is if this inspires you, if this gets you thinking of the box Oh, like I can't do these things normally because I have HIV. I'm limited into what supplements I can take. Maybe this will inspire you to talk to your doctor or to talk to a professional about it and see what your options actually are because you might be surprised. And with that said, I hope you enjoyed this vlog. Please, again, like, subscribe, share this with anybody that you think might find this useful and let me know what you think. Send me your comments, your questions. Let me know what else you want me to vlog and I'll talk to you guys soon. Alright, thanks. Night.