# Letter to the editor

## In validation of experiments to measure the speed of light using a microwave oven and chocolate bar

The purpose of this letter is to evaluate and validate the procedures described by Ford and Mason1 using a microwave oven and chocolate bar to measure the speed of light. Before addressing the experiment specifically I want to offer a couple of minor corrections regarding the statements made in the “Extension” section of the article. It is not quite true that holes smaller than 10 cm “…are too small for microwaves to leak out.” More accurately stated, holes smaller than approximately 7 cm are too small for microwaves (@ 2450 MHz) to pass through without being diminished in intensity (attenuated). Near 7 cm the rate of attenuation is very little, while attenuation increases as the holes get smaller. The key is that they have to be MUCH smaller than 7 cm (or the thickness of the mesh screen MUCH greater) for the microwaves passing through to be reduced to a safe level.2

The measurement technique described in the article is based on the concept that “hot spots” in a microwave oven are spaced roughly one-half of a wavelength apart from each other. Noting that these hot spots are “standing waves” created by electromagnetic waves reflecting upon themselves, this spacing may be applicable for waves propagating in free space but not necessarily within a closed resonant cavity such as that of a microwave oven. In fact, the apparently random distribution of hot spots within a microwave oven results in an equally random distribution of distances between them. While the theoretical distance between standing wave peaks for 2450 MHz microwave energy in free space is 6.1 cm, Figure 1 illustrates a wide variation of distances between hot spots within a microwave oven cavity. Using a single chocolate bar placed within this distribution can result in a measurement between melted spots that varies substantially from the theoretical distance.

However, by modifying the measurement method to use a larger area of chocolate, the basic technique to measure the speed of light may still be applicable. To confirm, chocolate morsels were melted and spread evenly across a large turntable, then cooled. The large chocolate disc was heated in a similar manner as described in the article. The turntable was set not to rotate. Because the amount of chocolate was so much greater than a single bar, the heating time was much longer — around 5 minutes. Others who repeat the experiment might use different amounts of chocolate, in which case the optimal heating time will vary.

Jelly beans (Champagne flavored) were placed at the centers of each identifiable melt spot (Fig. 2). Note that the degree of melting varied between spots, as would be suggested by the varying field intensity shown in Fig. 1. Additional melt spots may have appeared if the heating time had been extended. It should also be noted that field peaks exist in three-dimensional space and therefore could be located just above the surface of the chocolate.

By measuring the distances between melt spots it can be seen that the minimum distances are roughly in the neighborhood of 6 cm. The choice to use minimum distance basically comes from the notion that, for a given frequency, the distance between standing wave peaks will never be any less than one-half wavelength. Imagine the peaks evenly distributed in space as a cubic lattice in which all nearest neighbors are ½-wave apart. Then slice a plane through peaks that are not directly adjacent and imagine that plane being the sheet of chocolate. It is then easy to see that the melt spots created by peaks in the plane can be greater than ½-wave apart but never less than that. However, if a peak just off the plane is projected perpendicularly onto the plane (thus representing another melt spot), the new point could be less than ½-wave from the nearest peak that is in the plane (a fun lessons in geometry! These thus

Fig. 2: Distances (a) between melt spots in a large layer of chocolate on a turntable are identified by jelly beans (b).

could be differentiated from those created by peaks that are more directly in the plane. In any case, it’s important to keep in mind that the plane of chocolate will slice through an unknown irregular lattice structure at some unknown angle that will pick up some peaks while passing close to or far from others.

Shorter distances could be due to the existence of hot spots just above the chocolate surface and close enough to cause melting.

In conclusion, with proper understanding of the behavior of electromagnetic waves in a closed resonant cavity, it is shown that the speed of light can indeed be measured using a microwave oven and chocolate.

#### References

1.    R. Ford, D. Mason, Microwaving a chocolate bar, Chem 13 News, University of Waterloo, February 2018, pages 6-7.
2.     Application Bulleting: Cut-off Tube Design, Gerling Applied Engineering, Inc., Doc # 960005, March 2009.