Measuring the speed of light with a microwave oven

Moisés Montalvo Lafontaine

To measure the speed of an object we just need to know the time it takes the object to travel certain distance and use Newton’s law of motion. It sound simple and it is. But how the speed of light is measure using this technique? Well is hard to do it with accuracy because the speed of light is so high that the time it takes to travel some measurable distance is extremely small. So I wonder how it was measure. But most important to me is how I can measure it myself. Well it turns out to be easy to do and we all have the equipment to do it: the microwave oven.

First let’s explain the early attempts to measure the speed of light. Galileo tried to measure it using a lamp at a great distance but he concluded that the speed must be extremely high to be measure. To perform better measurements it was required a laboratory environment. Albert A. Michelson used the rotating mirror apparatus shown below. This had higher precision than previous ones and it gave Michelson a good value of the speed of light in the air. As we can see in the diagram the apparatus measurement was purely mechanical. But with this apparatus Albert A. Michelson performed measurements good to nearly one part in ten thousand. 

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With the advances in technology, better measures were made at the National Institute of Standards and Technology (NIST). This new techniques reduced 100-times the uncertainty for the value of the speed of light. Of course is not a technique as simple and mechanical as the early ones because it’s based in the atomic/molecular measurements using a helium-neon laser. The speed of light is defined to be 299,792,458 m/s (or 3 X 10^8 m/s when high precision is not require). Because this value is constant the meter was redefine in terms of the speed of light using the relation c=νλ. 

Like a mention before, we can calculate the speed of light using a microwave oven. We can do it theoretically or experimentally. The frequency v in a microwave oven is usually 2.45 gigahertz. At this frequency, water molecules resonates releasing heat. The distance from peak to peak of microwaves (wavelength λ) is almost 12.2 centimeters. So using the formula c=νλ we obtain c=(2.45X10^9 Hertz)*(0.122 m) = 2.989X10^8 m/s. This result was obtained using the theoretical values of the microwave oven operating frequency and wavelength. How can we determine this experimentally? First, and very important, we have to take out the rotating plate. What this plate does is rotate the food so it can be heat evenly because the microwaves are emitted “linearly”. Use cheese and microwave it for a couple of seconds. The cheese is going to melt but not uniformly. Is going to melt only in the spot were the microwave hits it. Measure the distance (in meters) between the centers of the spots. That distance is half the wavelength of the light so it has to be doubled in order to obtain λ = 0.122 m. Multiply that by the frequency of the microwave v = 2.45X10^9 Hertz and the velocity of light (in the air) is obtain.

http://www.scientificamerican.com/article.cfm?id=microwaves-and-the-speed

http://www.scientificamerican.com/article.cfm?id=how-the-microwave-works

http://www.scientificamerican.com/slideshow.cfm?id=how-the-microwave-works