Okay, cool, stay uncomfortable over here and be broke.    Yep. Searching for greatness in a sea of the time to shame this. A sea of the aimless. I don't wanna be one of the nameless. I'ma wake up with the mindset that we're seeing. This is when we all meet up and we test each other. This is test day. This is the combine. The combine is where the people train outside of the combine and they show up to run, right? Oh yeah. Let me give you an example. Do you sell? Yeah. Come here. Come here, I'm gonna show you some. This is combine 101 and sell. Just watch. What's your name? Cooper. How long you been selling for? I'm two years. Cool, what do you sell? My Toyota. Okay, you sell cars? Yes sir.   Hit me at the trial close, ask me to buy it. So if the number's lined up, is this the car that you would see yourself driving home today? No, I need to go home and think about it. I completely understand, there has been a lot to think about, but I haven't given you all the information that you needed. If you have five quick minutes, I can take the inside and give you the proposal so that we have all the info. Time out. We're going to test drive, we get off the test drive, we get back off the test drive. Hit me at the trial close. Again. Again, trial close. I totally understand. I haven't given you all the information. No, no, no, hit me at the trial close. Ask me to buy the car again. I'm going with another objection.  And I'm going to figure out where's breaking point is. Hit me at the trial close again. Andy, if I could get the deal right, would you be happy to take it home? So Andy, if I could get the numbers right, is this the car that you take home? I got a couple more cars I want to go look at. Thanks for letting me test drive it. I'm going to get back with you, go. I totally understand. As we were talking before, this is the first dealership that you've come to. Normally people go to the dealership that they like first. Look, you were just the closest to me. I got two more I want to go see. You were closest to me, so I came to you first. I'm going to go check out these other two. I'll get back with you. Okay. Hey guys, what's going on? It's Andy. A lot of you leave comments telling me that you need help. Do me a favor. I'm going to tell you the best way to get a hold of me. Shoot me a text message right now,<PHONE_NUMBER>.<PHONE_NUMBER>. I'll help you with whatever you need.  Let's get back to the video. Combine, combine. We didn't even get to run two races. We've been doing it two years. How many times have somebody told you they got a couple more cars they're going to look at and they're going to get back with you? Quite a bit. Quite a bit. Okay. Let's use common sense for a minute.  Dude, we didn't see that coming, man. What if I walked up to him again and I had my hand like this? You think you'd let me hit him twice? I got you. Okay. Okay. I got you back. He's been selling for two years. And in two years, almost every day he goes to work. Someone says, I got a couple more cars to go look at. I'm going to get back with you.  Because if he cared, he'd do something about it and you'd be great at it, right? Yes, sir. So you don't know it. And here we are two years in. How much money is the average car deal in a dealership? Say it's 500 bucks. Let's say he misses four deals a week, just four because of this objection. That's two grand, two times 52. Just do the math.  That's just hypothetically. Let's go through all the other objections. Okay. Tell me you got a couple more cars to go look at. I got a couple more cars to look at. Hey, number one, I totally understand. Let me ask you a question. Are the cars you're going to go look at similar to the ones that me and you just drove or completely different? Which one? I completely the same. So they're going to be the same? Yes, sir. Okay, hypothetically. Let's say that you went and looked at all the other vehicles. I don't care if there was two of them or 10 of them. And you spent all day driving them, every single one of them. And then let's say my beautiful 2018 Nissan Ultima with 38,000 miles per white black leather interior. Let's say it was the last one you went and looked at. After seeing every car, all of them, in the end, what would be the deciding factor on which one you ended up buying? Would it be the car itself, regardless of the deal or the great deal the dealership's willing to give you? Which one? The great deal. So it's not a matter of if you're gonna buy it's when and the when is when the deal's right, right? Cool, so if I could save you some time and money would that offend you in any way? Would you be upset with me at all? Not at all. Thank goodness.  Why? Because that's my job. When somebody does their job, that's like how they get to stay at their job.   And you're like, what's going on in there, man? That's what it's like walking into a sales company. Sales company's jobs are to make sales. Am I right? Right.    They already had their mind made up. Listen to me, you don't do anything but cost us money. Listen, my goal with all of you is this, get up here, show us you know it. If you don't know it, you better train or settle. That's it. You guys all have a choice today. We settle.   I'm uncomfortable over there, dude. I don't like that. Okay, cool, stay uncomfortable over here and be broke.  You'll die with regrets. Your kids will look up to someone else.    No ways. I'll stay over here and I'll fight. I will be coachable. That's a skill, by the way, to be coachable. I'll be coachable. I'll drop my pride, my ego, my entitlement. I'll be a sponge. Your student is here, teacher. Let's go.  And then, once I get it, I'm gonna keep elevating it my whole life but then I'm gonna teach it to my future team because a team can't be beat. Hey guys, that's what I'm gonna tell you. You're the true one percenters. You made it till the end of the video. Do me a favor, share it with the friend that wants to go to another level. Make sure you like the video. Comment below so I know who you are. Set your notifications and then subscribe to the channel. We got daily sales training videos dropping. I'll see you soon.


I gotta leave Vigino out front, he's actually kinda doing some work. He's a little fat, he's got the speed. Oh, Sinta! Yo, do me a favor, Kibbu! Never stand up again! How's it going, everybody? Dotted away here back with some more Dragon Ball Fighter's Ranked Matches. This time around, we're playing some Vigino Blue and the main team of Super Saiyan Goku and Yamcha, because somebody really wanted to see some Vigino Blue. Hopefully he stands out, dude, because if I lose another Ranked Match to somebody that's about to become a God of Destruction... Dude, I might go Super Saiyan Blue myself. It might be a sad time. I'm gonna throw out a Beam assist. Oh, no. It's already not going well. Never mind. We're gonna take a free hit here. I can't get much off of it, but we'll get just enough. We're gonna get to see how she plays on defense. Alright, then get out of the corner strict. We're on me extremely well. We gotta stay grounded there. The next time we get a hit, we gotta stay grounded. It might already be looking like it's time to spark, honestly. Alright, no, we actually get away. Man, I don't know how long I'm gonna be able to hold out. Damn. Gotta waste the bar here because I didn't get him all the way into the corner. And when you don't do that with Yamcha, you can't finish with a full heavy and then get away with it. So, he is gonna block here. Man, that is a real shame, huh? That is a real shame how I did that. No, the Kid Bootball! No! I let it 21 get away so many times! Do I go optimal? Do I go out? No, no, no. Hold on, hold on. Let me hold my horses. Let me get 21. Let me get 21 out. Beautiful tail by the 21. Just goes under. I wasn't blocking low. Kid Booh assist for the extension.  It would have changed the game for me.  Now we gotta start looking for sparking opportunities and everything like that. We're gonna go ahead and do it now. Okay, oh, I always try to jump. I gotta hold my ground against these Majin players. Have I been saying Majin 21? Hopefully I've been saying Android 21, because it's not Majin 21. Three bars will get the kill here on Yamcha. Gonna be smart and leave 21 out of the point position because any hit would kill on her from any other player. I would probably drop it. Oh, it was a late dash in for the overhead, but damn, it's not looking good. It's not looking good for your boy right now. Whoo, we actually get a Super Dash though.  And I think this person has very much seen that now. She kind of respected it at first like, oh man, okay, he's got the assist set up. Let me respect it. But now he sees I'm kind of just wildly throwing it out and I think I've lost that fear factor. Vegeta Blue, you are going to have to snap if we are gonna win this game, man. That was all me, bro. I'm sorry, I can't block a low to save my life right now. I think we're dead. Okay, okay, you know what?  I tried, oh, the dry gross panic actually worked. Get out of here. Mission accomplished boys, let's go home. And by home, I mean the loser's bracket. But we are out of here. I will see you later. Dark Ansel didn't block it. Okay, sick. I tried back dashing. That probably wasn't smart. I could have gotten a reflect there too. He was doing very good at making sure I never got a chance to reflect that, but right there I think I could have. Okay, well, here he goes up to God of Destruction. I am a failure. I've ranked up more people to God of Destruction than I would like to.  The play has switched. Look at the beam assist. Let's go, I'm starting to cook. Now you want to get aggressive, let's go. I'm trying to speed up the game myself. Oh, I messed up. Did I, though? Did I mess up? I did. Don't tell him that, though. As far as this guy knows, I'm going off right now. I'm using the effect that this is online to my full advantage. Nobody's taking Dragon Rush as a three-frame delay. He will start doing it very shortly, so it's time for us to change. Nice down heavy. Oh, that was beautiful. I'm starting to go into that mode that I go to in very close Dragon Ball Fighters matches, by the way. So I expect a lot of sound effects, a lot of me panicking, and that's pretty much it. Damn, my down heavy. Did it not work there for a reason? Oh, I tried it. Heavy didn't come out. I staggered it too slow. I wanted him to click a button, but I just did not pull it off as gracefully as I wanted to. Can he kill here? Probably, right? We stay living, though. I mean, let's go. That hitbox was kind of wild, but I'm not going to complain. My team is going really well right now. Who do I want out? Let's go. Gallic Gun. I got to leave Vegeta out front. He's actually kind of doing some work. He's a little fat. He's got the speed. Do me a favor, Kid Boo. Never stand up again.  Yo, this man is confident. You got to do better to open me up. Oh, okay. That's pretty good. That was pretty damn good. Nah. We're on the move now. Beautiful. That was really confident. If you could put me down, I know you want to use them, but let's not level three in a... Okay. So no bun. You didn't drag and rush. Okay, this guy is going off. It's always these one-character situations where I crack. Oh, God. They start playing so smart when they don't have three characters left. Maybe I got to get a little dumber. Is this game? Hold on. Hold on. One, two, three, four, five. That wasn't even five, but I should kill anyway, right? Yamachaa! The mode is... I'm kidding. I'm kidding. But I'm not on a certain level. On a certain level, I'm kidding. But on a certain level, I'm not. The mode him. Strip him of his title. Come on. Nah, we're not... Oh, that actually took a chunk of BP. Come here. I'm going... I plan on taking back what you took from me. True saying, never loses pride after all. I'm playing Gojida Blue. Oh, you would have thought. Okay. I'm having a good time, dude. High-level Dragon Ball fighters is a lot of fun. Ah! Jesus. I'm starting to have a great time. Let's go. You can tell I'm feeling myself, by the way. I'm clicking these buttons. Let's go. It's time. It's your boy. Come here. Gallant gun. It's Vegeta Blue time, baby. He's going to keep it mad basic, but it's going to be there. I might run up. I might run up to him. Okay. So, that was... Let's talk about how bad of an idea that was. Get another hit with the Yamcha, sis. We are cooking. We are cooking right now. I wish I would have 2M to start that. I wish I didn't waste time with that 2L, because it really didn't work. It didn't look good on me. Let's say how it really is. No way! Oh, beautiful play. I just hate myself so much right now. Hold on. Let me come back. Let me come back. An air level thr... So, this is embarrassing. Uh... You have seen that I'm a scrub. Uh, I fully admit, perhaps it wasn't the most dignified option. Man, I wasted spark and 3 bars. Let's not talk about it. Let's not talk about it. Oh, do I even go... No, I'm not going to go for the optimal. I want to win. I want to win more than I want to show off progress. Okay. Okay.  I'm not going to lie. Not the best time I've ever had. Oh! What the... Why the grab? What level of rea... What parallel universe did I just get grabbed on? Oh, beautiful dashing. It's going to be down to Yamcha. Man, this game started off so good for us too. Man, I cracked mid-game. We'll try again. We'll try again next time. Game. I'm speaking like I'm giving up. I'm not... I've not given up just yet. It's clear that kid booze is my problem character. But I think I've always known that. Let's see if Yamcha can get the job then. Damn, so slow. All right. Hold on. Let's keep it mad basic. I was going to go for the dragon balls. I'll fully admit. But let's just... Let's just try to make a comeback here. Okay. Not going to get nearly the borrow I would need to kill here, but we can go for another mix. We can go for one more mix. I don't see the problem. I'm going to go with a 2M. That was so close to being bad for us. Don't get a... Don't... Okay. He could... And I'm not happy about that. Don't do it. Don't do it. You wouldn't. Why are you doing this? He's doing it. Oh, you needed one more bar. A ball. All right. He was just winning then. Never mind. I thought he was trying to embarrass me. Which I would have been okay with. If he would have pulled off a Shenron combo.  That would have been... That would have been hype. Okay. We can still demote him if we get a win here. Man, that's exciting. We started so strong. Okay. Great start. I didn't want to go with the beam assist. And another great start. Let's go. Let's go. You're wondering why I didn't do the optimal one. It's just because I didn't feel comfortable. I thought I would drop it. I don't know why I thought I would drop it. Because I did it fine last time, but... Another good hit. Come on. Let's just keep the tempo going. Is he going to spark because my tempo is too high? I think so. No, he wasn't. My tempo didn't bother him. My tempo did not bother him at all.   Let's go. We're coming up on the... Of what could be... Of what could be the one. Beautiful 2M. Oh, I wish I was blocking high. Damn it. Oh, great. Not enough bar. Let's go. Is it going to be enough? It's probably not going to be not with the... Come on, Blue Vegeta. About that God of destruction title. I'm going to have to... I'm going to have to snatch that back real quick. Give me... Give me that back. Nobody ranks up against me. He gets away except for the last guy and the guy before that and the guy before that. But other than that, nobody gets away. Oh, no. Are he playing serious? He can win. Oh, god. Yeah, two hits. Two overheads. That was too much for me. I need help. Why is he playing so... Get after him. Get after him. Let's keep it optimal, shall we? I hate myself. Dropped it at the last... How do you drop it at the super part of the combo? It's just an input. It's a quarter circle forward. I've been doing it since I was in diapers. Oh, this game. Damn, not the kid boo. And the sparking healed Android 21 up to... Damn near full. Oh, god. I'm going to raw switch. Goodbye, Jan. Oh, hey. Flash within EX ball. That was smart. Going to keep me in the corner. Yikes. Back out. Mmm, the low got me. I was going for a reflect. Six bars built up. How many Dragon Balls? Can I get a Dragon Ball check on all three? Nice plot. Okay. His tempo is crazy. Remember how last game I thought my tempo would be bothering him? No. No. No. It was bothering me. It was bothering me. Okay, we took up quite the beating there. Whoa, that caught my back. He's going to level three. Yep. Oh, damn. Is this the true difference between our skill? I might wake up level five. I might wake up level three. Okay. I try to do it. Okay. I want to at least make this a little bit less embarrassing. I don't know if my goal will ever be... That was good. This guy's a great player, dude. This guy's great. Oh, hello. Hello. A chance. The real come out, man. That was good. Double 2M Strat. Damn it. I could have killed. I got hit by so many Key Blast. Unless it drops, this is pretty much the game. And that's going to be the set, too. It's got to be hard to stay. I got a destruction rank, to be honest. But good games to my opponent. Great games, even. What a set. I don't know what to title this. I don't know what... To say? I don't know what stamp I would put. I'm going to have to... That was a good fight. Yeah. I think I had that stamp, too. Thank you so much, man. That was great. You really bested me that last set. And I think if we played more, I probably would have kept losing. Man, what a time.  Really, these are like the cream of the crop. If you did, definitely make sure to go down below. Leave a like and subscribe to the channel to stay up to date on all things Dragon Ball Fighters. At this point, we should only be a couple days away from World Tour Finals and all the announcements. So definitely subscribe if you want to stick around to keep up to date on all that news. You can also watch more videos on your screen right now if you're into those. But other than that, I've been Dr. Dewey. Thanks for watching all the way to the end. And I will see you in the next one.


Hi everyone we're making lemon pasta with garlic and basil. Now this is a great quick easy recipe to make anytime it takes just a few minutes to put together and you have a nice dinner. You can also add some grilled shrimp to this or chicken if you want but it's definitely a standalone pasta dish that you're gonna love and I'm also using bonza pasta just to lower the carbs a bit add a little more protein and a little more fiber. So I'm Rockin Robin and I'm gonna show you how to make it right after this. Alright let's start off with our chef joke and I have another one for you a little bit later so stay tuned for that. Alright so how did the pasta chef get locked out of his house? He came home with gnocchi. Let me go over our ingredients so we can get started. So first up is like I mentioned earlier we're using bonza pasta we're using the spaghetti version that they have it's a chickpea pasta in case you're not familiar. After that we're gonna need some garlic that's our garlic and that I just chopped this up nice and fresh and you want it nice and fine I like it minced. I'm using some half and half now I've had this question before some people don't know what half and half is half and half is half milk and half cream it's not quite so rich is heavy cream so we'll be using that. I'm using some pecorino romano here I just grated up some and you can use parmesan if you like.  Then I want to cut these up into bite-sized pieces and we're gonna be sauteing these a little bit later. I'll be using a couple of organic lemons we're gonna be using the zest from this and the juice. I'm gonna need a couple of tablespoons of I have pastured butter here this is a carry-gold butter we'll be using some fresh basil which we have right here and some fresh Italian parsley. So with the basil we're just gonna stack the leaves here it makes it easier to roll and then slice and I'll just continue that until I get all this chopped up. So with the parsley what you want to do is just take your knife and sort of shave off the leaves so you minimize the stems and then you just chop it up and we'll need some salt and olive oil. Time for chef joke number two what happens when life gives you pickles instead of lemons you deal with it. So I want to recommend that you get everything set up and ready to go like I've got it here I've got all everything cut up shredded you know prepared and measured before I start this recipe because it cooks up really quickly. Now here's my pan we're gonna be cooking everything and right back here I have some water boiling getting it ready for my pasta so I can cook it. So I've got my pan here I'm gonna start out with medium-high heat and I'm gonna add some olive oil to the pan and to that I'm gonna add the asparagus because it's gonna take just a couple of minutes we're gonna cook this for about three maybe four minutes no more just wanted to get it a little tender. So the pasta takes about 8 to 10 minutes that's what it says on the package I want to cook it just a little al dente so I'm gonna go for 7 minutes and since all of this isn't going to take very long I'm gonna start that now so I just dump the pasta into some salted water and we're gonna let that cook I'm gonna turn the temperature down a little bit on the asparagus because it's taken off pretty good asparagus has been cooking three minutes you can always test it with a fork and see how it is if it's real crisp or if it's just about right and ready to go because it's gonna cook a little bit more as we continue on and that's feeling pretty good it's somewhere between three and four minutes depending on how thick your asparagus is obviously thicker is going to take longer all right I'm gonna add the butter to the pan now let's get that in there once that butter melts we're gonna add our garlic this is going to mellow out the flavor and just make this taste amazing now I'm on medium low heat and now I'm starting to smell that garlic whoo that smells so good give that one minute we don't want to we don't need to saute this very long that garlic we don't want it to burn I'm gonna turn the heat to low on the asparagus and we're gonna start adding our other ingredients so here's the cream here's our lemon juice our lemon zest mix it all around I want to bring this up to a simmer I'm gonna add a pinch of salt to this maybe about a half a teaspoon or so you can always taste it we'll taste it a little bit later and see how it's doing you can see now this has come to a simmer so I'm gonna turn it down again and I'm gonna add the basil and the cheese and that's gonna help to thicken up the sauce as well as that cream now you can give it a taste and you can adjust for salt if you wish I'm gonna add just another pinch of salt to that and it is now pretty much ready to accept the noodles but we're just waiting on those to finish up which will be in a well right now so I'm testing the pasta and it is just a touch al dente so it's perfect so I drained and rinse the noodles as per directions and now I'm gonna add them to the sauce all right you want to take some tongs and then we're just gonna drop this pasta right into the pan and that sauce is gonna absorb right into all that pasta now you take your tongs and you just give it the best stir you can just want to mix all that beautiful sauce into this now let me serve some of this up and we'll garnish with a little bit of fresh parsley and here we go so delicious nice lemony flavor that garlic comes through nice and subtle very delicious so if you'd like to add some garlic bread to this recipe you know it would be great I have a recipe for you got to try it out it's very popular I'll leave a link right over here for my ultimate garlic bread with roasted garlic so delicious you got to try it thank you so much for watching don't forget to subscribe to my channel smash the like button for me and leave me a comment we'll see you next time


Many civilizations have been and gone here upon our planet, yet thanks to the time within history in which certain civilizations flourished, countless artifacts and historical studies can and have been undertaken into their existence. We are able to decipher their daily lives, their religious beliefs and practices, even their languages. However, in doing so, we have never been able to decode any knowledge or explanation for the countless seemingly impossible ancient feats lost abilities of stone masonry, no documentation found within any hieroglyph, literature, parchment or other ancient text. Yet pyramids, polygonal masonry, multi-thousand-ton megaliths, along with countless other curious clear signatures of a lost civilization's work exists, and due to this mystery regarding how these sites were created, we have to presume that those who constructed them were placed at a far earlier time within history, one that was prior to a global flood, possibly the aftermath of a near-extinction level event, manifesting as a form of global amnesia and severing connections between continents, possibly for 10,000 years. Segesta within Sicily not only looks the same age as that of the foundation walls of Balback, and indeed the gargantuan megaliths found within the trilithon, but the enormous temple is still standing along with its amphitheater, which, if we look to the still surviving polygonal stage flooring present at the theater within Delphi, a site we have covered in the past, one which is also littered with polygonal walls. We find more support for the theory that these amphitheaters, with their incredible acoustics, are also remnants left by this same lost civilization. Yet we feel the smoking gun are the pertuberances which are still visible within its foundation blocks. It is of no surprise to us that its origins are hotly contested, with many academic teams concluding that it was merely the work of traveling Trojans, this regardless of the multi-ton columns that were so perfectly laid, they all still stand to this day. When one considers that pertuberances are found on polygonal masonry all around the world, and that modern stone masons are now exploring interlocking blocks with some such as large lego blocks already in mass production, it is no surprise that while many claim it to be Greek, others claim it not, this will not cease anytime soon. Many religious beliefs have gained traction in regard to its original purpose, thus conveniently there is little chance that this contention will move forward. Who built the ruins of Sagesta? When did they build them? We find the possibilities highly compelling.


Welcome to the 21st lecture in the course Engineering Electromagnetics. In this lecture we continue with our discussion on reflection and refraction of waves and the topic for discussion today is what is called the plane slab. You would recall that so far what we have discussed is the case of a single interface on either side of which we had infinite media. But if let us say the medium on which the plane wave is incident is of a finite extent then one can easily visualize that the wave is going to encounter two interfaces instead of one. And therefore, the interaction of the wave with the interfaces is going to be more complex and such a case is known of the case of a plane slab. The slab could be made of any material in general, but as we will see to derive some special results we will consider that the slab is made of perfect dielectric material. The slab is represented in the following manner. We consider that this is an interface between say medium 1 and medium 2 and medium 2 is in the form of a slab. So, that this is an interface between medium 2 and medium 3 and medium 2 extends over a width which may be D. And therefore, this is the thickness D is the thickness of the plane slab in medium 2. We will consider the case of normal incidents. The case of oblique incidents can also be considered, but is going to be more complicated. So, we consider the case of normal incidents of a uniform plane wave on such a slab from medium 1. Let us say that the incident wave represented by say E i is incident like this and we are showing it incident in this manner for the sake of clarity. Otherwise, the wave is incident at a normal angle. Now, part of the wave is going to be reflected back at this interface which we may call are 1 2. Please take note of the convention or the notation. 1 2 represents the reflection at the interface between media 1 and 2 for a wave travelling from medium 1 to medium 2. While part of the wave is going to be reflected back part of the wave is going to be transmitted into medium 2. Let us say it is transmitted in this manner and what is transmitted may be called as E t 1 2 following our convention. So, that when this transmitted wave travels to the second interface, it will have got changed in its phase by an amount equivalent to the phase shift constant of medium 2 and the thickness or the distance that is travelled in medium 2. Let the phase shift constant medium 2 be k 2. So, that by the time it reaches the other interface it becomes E t 1 2 E to the power minus j k 2 times d. Now, at this interface again part of the wave is going to be transmitted which may be called E t and following our convention E t 2 3 and part of the wave is going to be reflected back. Let us say like this where this may be called E r 2 3. So, what reaches here is therefore, E r 2 3 E to the power minus j k 2 d where once again part of it is going to be transmitted through becoming E t 2 1 following our convention and part of the wave is going to be reflected back in this manner and what is reflected back may be called E r 2 1 which when which upon reaching here becomes E r 2 1 E to the power minus j k 2 d and part of it is transmitted through becoming E t 2 3 prime and part of it is reflected back becoming E r 2 3 prime and becoming E r 2 3 prime E to the power minus j k 2 d and this is E r 2 1 prime etcetera. This becomes E t 2 1 prime and this series of reflections and transmissions is going to continue and as I mentioned it is only for the sake of clarity that the wave parts are being shown inclined to the interface plates otherwise all these reflections transmissions and the wave incidence are normal to these interfaces. See the convention that we have been following for the phase shift is always that in the direction of travel the phase is going to decrease. So, we are being consistent in following that convention otherwise you have rightly notice that the direction of propagation of this wave is opposite to that of the other wave but the wave you put down the phase shift it is alright. Now since the various reflections and transmissions are going to be governed by the reflection coefficient and the transmission coefficient at the various interfaces let us put down these coefficients. We will have first let us say r 1 2 using the notation that r 1 2 is the reflection coefficient for a wave travelling from medium 1 into medium 2 which will be equal to eta 2 minus eta 1 upon eta 2 plus eta 1 assuming that the eta's are the intrinsic impedances of the two media. Similarly, t 1 2 as we know is going to be 1 plus r 1 2 on the other hand what will be r 2 1 reflection coefficient for a wave incident on the interface between media 2 and 1 travelling from medium 2 that will be eta 1 minus eta 2 upon eta 1 plus eta 2. So, that it is minus r 1 2 and accordingly t 2 1 the transmission in a similar situation is going to be 1 plus r 2 1.  So, armed with this picture and these coefficients reflection and transmission coefficients we can now consider what is the overall reflection back into medium 1 and what is the overall transmission through the plate slab. We will have to consider these various contributions for reflection let us say and the various contributions for transmission, but if you proceed systematically it will be possible to come to a simple result. Let us consider what is reflected back in medium 1. The first term in the series of various reflections that are going to be added to find out the overall reflection is going to be E r 1 2 which is going to be r 1 2 times E i. The second term is going to be E t 2 1 which is going to be t 2 1 into E r 2 3 e to the power minus j k 2 d and then E r 2 3 can be traced back to E i through a reflection here and transmission here and two phase shifts with magnitude k 2 d. So, on this basis E t 2 1 can be written as t 2 1 times r 2 3 times t 1 2 and e to the power minus 2 j k 2 d times E i this becomes our let us say equation 1 this is equation 2. Next let us put down E r 2 1 in terms of this we will be able to get E t 2 1 prime and therefore, let us put down E r 2 1 which is going to be r 2 1 and then E r 2 3 e to the power minus j k 2 d and therefore, in the above expression if we interchange t 2 1 and r 2 1 we should get E r 2 1 and doing exactly that we get this as r 2 1 2 3 t 1 2 e to the power minus 2 j k 2 d into E i which may be equation 3. In terms of E r 2 1 now we can get E t 2 1 prime E t 2 1 prime is going to be t 2 1 E r 2 3 prime e to the power minus j k 2 d and tracing the series of reflections and transmissions one can make out that E t 2 1 prime can be written in two parts as t 2 1 r 2 3 times t 1 2 e to the power minus 2 j k 2 d this becomes the first part in the expression for E t 2 1 prime and the second part becomes r 2 1 r 2 3 e to the power minus 2 j k 2 d times of course, E i which may be equation 4. Similarly, one can put down E r 2 1 prime which is going to be r 2 1 r 2 3 t 1 2 e to the power minus 2 j k 2 d times r 2 1 r 2 3 e to the power minus 2 j k 2 d into E i which is equation 5. If you have any questions we can tackle those now. It is the product of this term and this term. Let us say we are talking about E t 2 1 prime E t 2 1 prime is this and we are writing it in terms of E i. So, you can start at this point t 1 2 then r 2 3 then r 2 1 and then r 2 3 and then t 2 1. So, this will be the coefficients and then the travels that we made 1 2 3 4 travels that we made phase shifts corresponding to those. So, this way it is possible to check the final result that we have reached. It will come you just check t 2 1 is here in any case. This is the final term that will come final coefficient. Sir, the phase shift because of reflection there will be some phase shift. No, whatever phase shifts are there because of reflection and transmission those are taken into account in the coefficients. So, we do not need to talk about those phase shifts. We are multiplying by the coefficients. If they are real there is no phase shift. If they are complex they will contribute their phase shift appropriately. So, now this way if we consider E t 2 1 and E t 2 1 prime it is possible to see a pattern. There will be a common term and there will be a common ratio of these various terms which constitute an infinite series. And therefore, we can say that E r which is going to be E r 1 2 plus E t 2 1 plus E t 2 1 prime etcetera. So, that E r by E i will be equal to E t 2 1 prime e i which is the reflection coefficient that we are interested in. We may call it rho or small r. Rho is the symbol we have been using earlier and small r is what we have used for the other component coefficients in this case. That is only a matter of notation. So, E r by E i is going to be equal to as one can see from there r 1 2 plus A plus A s squared etcetera.    Next, we are going to be looking at the summation we write the transmission coefficients in terms of the reflection coefficients just to reduce the number of variables or the quantities which need to be calculated in this expression.   Using the space on the left hand side this can be simplified and we get the expression for rho as r 2 3 times the exponent and then r 1 2 in the numerator r 1 2 plus r 2 3 e to the power minus 2 j k 2 d divided by the same numerator denominator that is 1 plus r 1 2 r 2 3 e to the power minus 2 j k 2 d which expression is quite compact even though we have added an infinite series. To interpret this expression and to see how it could be utilized in practice let us simplify it further and let us now make the assumption that the media that we are dealing with are perfect dielectrics. What will be the simplification caused by this? If the media are perfect dielectrics then these various coefficients are completely real and therefore, we can now consider the magnitude of rho or magnitude of rho square. Since, these coefficients are all real now we need to worry about only the exponential term and we get r 1 2 whole squared plus r 2 3 whole squared plus 2 r 1 2 r 2 3 cosine of 2 k to d in the numerator considering that magnitude squared is the square of the real part plus the square of the imaginary part.  And now one can derive or obtain a very useful application of this expression. We pose the question that for such a plane slab for such a situation involving three media is it possible to eliminate reflections completely that is is it possible to have magnitude rho squared or rho equal to 0. And for that purpose we will just put the we will try to see when the numerator becomes equal to 0. And it is possible to make the numerator 0 if we have r 1 2 equal to r 2 3 and also if we have cosine of 2 k to d equal to minus 1. Both conditions are required to make the reflection coefficient numerator equal to 0. Let us consider the implication of these conditions. The expressions for r 1 2 and r 2 3 are here and therefore, we just write down eta 2 minus eta 1 upon eta 2 plus eta 1 should be equal to eta 3 minus eta 2 upon eta 3 plus eta 2. And since we have already made the assumption that we are dealing with perfect electrics eta can be replaced by the corresponding epsilon or the permittivities square root of the permittivities.  And here we have root epsilon 2 minus root epsilon 3 upon the summation of the same terms which is the simple result that epsilon 1 upon epsilon 2 is equal to epsilon 2 upon epsilon 3 or epsilon 2 is equal to the geometric mean of epsilon 1 and epsilon 3. We have obtained this kind of result in a different context earlier. In the context of a quieter wave matching section on a transmission line and here also you see that somewhat similar result is coming. So, this correspondence between the plane wave phenomena and the transmission line phenomena we shall draw upon we shall make more formal a little later. But, right now let us just notice the similarity. So, if the permittivity of medium 2 is related to the permittivities of the medium on the either side then this is one of the conditions for eliminating reflections back into medium 1. What is the implication of the second condition? This amounts to saying that twice k 2 d is equal to an odd multiple of pi radians. So, that it is 2 m plus 1 into pi yielding a condition on d that d is equal to 2 m plus 1 into pi by 2 k 2, where what is k 2 d 2 k 2 is the phase shift constant in medium 2. So, that it is 2 pi by lambda 2 and using this result it becomes 2 m plus 1 by 4 into lambda 2, where lambda 2 is the wave length in medium 2 and can be further related to the wave length in free space as lambda naught by square root of the dielectric constant of medium 2 for the simple case that we are considering that the media are perfect dielectrics. So, that this is a standard relation for the wave length in a certain medium for a uniform plane wave to the wave length in free space in terms of the square root of the dielectric constant. Not only for perfect dielectric constant. Well, wherever the velocity can be written as the 1 by square root of mu epsilon there this result will hold. Therefore, just to be on the safe side we are saying that for perfect dielectrics this is the wave length. k 2 is serving the same role as beta for this medium. So, that it is omega square root of mu 2 epsilon 2 for the perfect dielectric that we are considering it to be. That is lambda naught by epsilon 1 2 epsilon r 2 relative permittivity of the second medium lambda naught is the wave length in free space for the frequency of the incident phase. The result that we have derived here says that in such a situation the reflections can be completely avoided provided the permittivities are related like this. And the second medium has a thickness which is an odd multiple of quarter wave length where the wave length is the wave length in the medium 2 which again is a result very similar to what we obtained for the quarter wave matching section. And as we mentioned there this concept is utilized very frequently in eliminating reflections from lenses and other optical items. And this is the basis of what is called the anti reflection coating. Although as we consider this more deeply it becomes clear that the anti reflection coating will have 0 reflection only at the design wave length. Only where the thickness of the coating satisfies this relation that it is it is an odd multiple of quarter wave length where the wave length is the wave length in that medium. Apart from acting as an anti reflection coating in the context of optical elements this concept can be utilized for reducing reflections from aircraft and missiles also. So, that they become less easily detectable by the enemy radars used in this context that is for reducing the reflections from the point of view of radar takes us into what is called the radar absorbing material field. A ram is a radar absorbing material and this concept applied to that will imply that if we have a suitable coating on the surface of the aircraft or on the surface of the missile satisfying these conditions it will be possible to also become obvious as we pondered about it. First of all the reflection will be 0 only at particular wave lengths or only at particular frequencies. And secondly the results have been derived for the case of normal incidence and when these conditions are not maintained obviously the coating is going to be some reflection. And therefore, I am guessing a little bit here what may be more useful from the point of view of radar absorbing material which acts over a broader range of frequencies is perhaps an arrangement which would be like this. So, we have a missile and we provide a coating, a coating is hand insaturated for the sake of the similarity which has a mu and epsilon such that their ratio is equal to the intrinsic impedance of the three states. So, that eta naught is equal to square root of the mu by epsilon or if the medium is conducting in the more general case it is j omega mu upon sigma plus j omega epsilon. In which case reflections on this interface can be avoided over a very broad range of frequencies further if the medium is made lossy. So, these mu and epsilon down the r of the coating. If you like you could put subscript c to show very clearly that these are the properties of the medium which is being used for coating purposes. Now, this only ensures that there is no reflection at this interface, but part of the way but the way that enters here will be reflected back and will be available for the reflection purposes. So, this does not serve the purpose. So, if the medium is lossy and if the medium is such that it provides sufficient loss. So, that the way which is travelled this part in this medium is sufficiently reduced in amplitude. Then the reflections can be considerably avoided. So, development of this kind of data and all the materials which are effective for a broad range of frequencies is the of a great strategic importance from the point of view of difference. And this active area research. Now, let us proceed further and consider once again the expression for the reflection coefficient that we have derived earlier magnitude of those squared. And this time we write the reflection coefficient magnitude squared for another special case where let us say medium 1 is the same as medium 3. What is the effect on these coefficients for this? We will have R 2 3 equal to 1 2 for this case. You just replace eta 3 by eta 1 and the result is obvious.  And it simplifies to be 4 R 1 2 4 squared and then the sine of k to d divided by the same.  And in this case that is when media on either side of the plane slump are identical. The reflection coefficient is going to be 0 when k to d is going to be a multiple of pi ray beams that is k to d equal to n pi f equal to n integer. So, that d is the point is equal to n times pi by d 2 and as before since k 2 is 2 pi by lambda 2. What we get here is n times lambda 2 by 2 with lambda 2 once again be equal to lambda naught square root of r. And we find that if the thickness of the second medium for this condition is a multiple of half paper half lambda 2 then also there are no reflections back into medium 1. This kind of a slab plane slab satisfying this condition is called a half wave plane or a half wave plane plane. And what we saw earlier which could serve as an anti reflection protein is called a quarter wave plane. What could be the applications of this observation? What is the observation? The observation is that if we have to if the middle medium on the either side of a plane slab and the plane slab is multiple of half wave plane thickness then there are no reflections either for a wave incident from medium 3 or for a wave incident from medium 1. So, this observation is utilized in the making what are called ray domes. A ray dome can be considered to be a derived from a combination of two words. Let us say dome for a radar and it provides environmental protection to the antenna, antenna of a radar or of a communication system. You know that the antenna is exposed to the severities of the weather and therefore its performance can degrade with course of time or let us say when rain or snow fall on the antenna surface. And these problems can be avoided by putting what is called a ray dome. And let us consider a usual dish antenna which would have seen in many places let us say it looks like this. It is actually a parabolic reflector antenna then it has a feature which is called a baffle which we can discuss later. And now if you put a window here which at the operating frequency or which at the operating frequency is a half wave plane or multiple of a half wave plane then it will be completely transparent through the signals that are transmitted or through the signals that are received providing at the same time environmental protection to this antenna. The rados can take many different shapes depending on the application or depending on the requirements. For example, if the antenna is required to be rotated then one could put a spherical ray dome covering the entire antenna or else to reduce cost it may be there is a window in this manner. And sure you can recognize this shape and you have seen this on top of many buildings in detail. So, the purpose of this dielectric window is to provide environmental protection and to remain transparent at the same time. So, the artwork that we had done in the dielectric reflection coefficient had these two obviously very interesting and important applications. One is in providing anti reflection coating and the other is in providing protection to antennas in communication systems and radars. Now, we can proceed further and consider the total field that is transmitted through the laser. In this case we proceed in a similar manner and consider the addition of ray types which are t equal to t to 3 plus e t to 3 prime plus e t to 3 double prime plus e t to 3 double prime etcetera which again is an infinite series. And the expressions for these various components in the series various terms in the series can be worked out in a very similar manner as we did for finding out the reflection coefficient. And on that basis when we try out the transmission coefficient which is going to be e t y in this case also it turns out to be a dielectric progression with terms reading as a 1 plus a 1 s plus a 1 s square etcetera. Where a 1 is t 1 to t 2 3 e to the prime power minus j k 2 t and s remains the same value as earlier that is r 2 1 r 2 3 e to the power minus 2 j k 2 t. So, that the transmission coefficient is a 1 upon 1 minus s that is t 1 to t 2 3 e to the power minus j k 2 t t 2 minus j k 2 t a 2 single without the factor of 3. That can be made out from the first term here there is a single phase shift in the first term.  Making substitutions as before expressing the transmission coefficients in terms of the reflected coefficients one obtains that some of the simpler expression for the transmission coefficient means 1 plus r 1 2 into 1 plus r 2 3 e to the power minus j k 2 t upon 1 plus r 1 2 times r 2 3 e to the power minus 2 j more or less complete our discussion on the feature called slag. Now, here we have derived these results for the reflection coefficient and the transmission coefficient considering a series of reflections and transmissions which provides a somewhat clear inside into what is actually happening inside the plane slab where we have interactions of the wave with two interfaces. However, there are alternative methods available which are less tedious, but they do not incorporate this kind of clear understanding. Before we stop let me pose a question. Supposing we are required to find out the total power transmitted through such a slab and what are we going to be required to be 2. One straight forward method as the answer has come is to calculate the transmission coefficient and hence calculate the pointing vector, but if we already have calculated the reflection coefficient then it is not really necessary. We just calculate what is the power reflected back and if you assume that the plane slab is non-absorbing, it is not lossy then whatever is not reflected back is going to be transmitted through the plane slab. So, this is where we like to stop unless we have some questions. Sir, this is 1 minus r mu 2. No. Sir, yes. Just write out. Sir, after a different number of reflections, the entire layer has been detected on pressure proof. So, e t plus e r should be e. Okay, it is fine if we can discuss that now and then we can go ahead. Let us stop here.