Friday, February 3, 2012

Measuring the speed of light with microwave

in this experiment we will measure the speed of light with microwave and chocolate . This is a great experiment for kids. One way is to measure how long it takes, from opening a packet of chocolate to the moment the kids finish it. This is indeed very high speed but still less than the speed of light. The speed of light is one of the most important constants of nature science in general and astronomy in particular but measuring it was a challenge which required complicated experiments.

Today you can conduct an experiment and obtain a very accurate value for the speed of light using nothing but a domestic microwave oven and chocolate bars. The experiment is suitable for children of all ages. First we will describe the experiment and then explain the physics behind it.
Required equipment:
Microwave oven – Almost any microwave will be suitable. Microwaves in which the revolving plate cannot be removed or have more than one radiation source, do not qualify. You must check the frequency of the oven. The frequency usually appears on a sticker at the back of the oven. Most ovens work at a frequency of 2450MHz but it is worth checking anyway.
Note frequency (2450)
Note the frequency 2450Mhz

To perform the experiment you must be able to remove the revolving plate from the microwave and place the chocolate bar on a plate in parallel to the door as sjhown in the following picture:
The chocolate lying in the microwave

Start the microwave at maximum power for half a minute to let some of the chocolate melt, remove carefully and put on a flat surface.
Please note that there are places that the melting is observable (three places) and other places did not melt at all. Find the distance between two places which have not melted at all. From the photo, the distance is about 6cm (2.362 inches)
Measure between two non-melted places in the chocolate

All that's left to do is simple arithmetic:
(Distance * 2 * frequency) divided by (100,000) KM/Sec which is to be used if the distance is measured in centimeters
(Distance * 2 * frequency) divided by (77,335) Miles/Sec which is used for distance in inches

In our example (sorry U.S. guys, the metric system rules!):
(6*2*2450,000,000)/100,000 = 294,000 KM/second (~182000 Miles/Sec). Amazing.
Why does it work?
Electromagnetic waves are moving at the speed of light (almost, it is little less due to the air, but it really does not matter for the experiment). Microwave structure causes the wave to be a standing wave.
Standing wave - Source: Wikipedia
Notice the red dots on the wave, which always remain at the same height. Where there is no movement there is no heat and energy. Also, there are the peaks of the wave, at which the warming will be greatest. For this reason there are rotating plates in the microwave so the food will be evenly heated.
The photo shows that the distance between two points with zero energy is exactly equal to half of the wavelength. These are the places where the chocolate has not melted at all. The Wave formula says that the wave length * number of waves (frequency) = wave speed.
So we get the frequency from the microwave manufacturer, the wavelength, we measured with the chocolate. All we need is to put them into the formula (division is to transfer from centimeters to kilometers) and get an amazing precise result for the speed of light.