How to measure the speed of light using chocolate and a microwave

Thanks to the advent of modern technology it is now possible for the common man to measure the speed of light within the confines of the kitchen. Yes, now you too can measure a quantity that had plagued science for hundreds of years.

To perform this experiment you will need the following:

Equipment

Bar of Chocolate: dimensions greater than 18 cm x 8 cm

Standard Consumer Microwave Oven

Paper Towel

Tooth Picks

Ruler with centimeter measurement

Procedure

Examine the microwave, the rear surface as well as inside the door, looking for a label stating the frequency. If there is no label containing this value, the majority of microwave ovens operate at 2.45 gigahertz. If the microwave has a rotating turn table remove or disable it. Remove the packaging from the chocolate and place on top of a piece of paper towel on a plate Place the plate with the paper towel and the chocolate in the microwave, so that the chocolate is positioned with the longest sides facing the longest sides of the microwave. Heat the chocolate in the microwave until it barely begins to melt, pausing the oven to check occasionally (the time will vary with the oven, from 20 seconds to 90 seconds) Once the chocolate has begun to melt remove it from the microwave, probe the surface for a pattern of hot melted spots, about the dimensions of a dime. Use toothpicks to mark the hotspots, placing them in the center of the hotspots. Measure the distance between the toothpicks, recording the data.

A note of safety: It is possible to damage a microwave oven by trying to heat an inadequate amount of material, although highly unlikely in this case, if you are concerned this can be avoided by placing a pyrex vessel filled with water in the microwave as well as the chocolate.

How this works

To heat food, the microwave oven creates a series of standing microwaves, which excite water, fat, and sugar molecules, creating atomic motion, or heat. In order to create standing waves the microwave is built so that the length of the interior is a multiple of the wavelengths of the microwaves. This creates a pattern of hot spots where the microwave causes more atomic motion, these hot spots are the crests and troughs of the microwave, and the cooler spots are the areas in between. The greatest heating occurs where the waves have the greatest amplitude; because this is a standing wave this area remains the same. When you measure the distance between two hotspots this is the distance from crest to trough or of half a wavelength.

Because we know the frequency of the wave ( f ), as well as the wave length ( λ ) (distance between two hotspots multiplied by 2) we can calculate the speed of the wave, which, being an electromagnetic wave, travels at the speed of light ( c ), using the formula:

c = λ * f

Sample Calculation:

Measurement of hotspot distance = 6.1 cm

λ = .061 m * 2 = .122 m

.122 m * 2.45e9 hz = 298900000 m/s

In sigfigs 299000000 m/s. This value is incredibly close to the actual speed of light, considering the error involved in the methods used.

Once you finish this calculation you have successfully measured the speed of light, through a bar of chocolate. The accepted value for c (the speeed of light) in a vacuum is 299,792,458 m/s.

Additional Tip: Grating the chocolate may give more precise results due to the greater surface area and less conduction of heat. Thanks to Shen for the tip!