# the speed of light in chocolate

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OK I read on another part of the forum about the determination of the speed of light using a chocolate bar and a microwave,

My and my students tried this out today and came up with a value of 2.2 x 10^8 m/s.

originally I thought that most of this error comes from the dodginess of the measurement and from the inaccuracy of the frequency on the back of the microwave. however, I asked my students about the sources of error and one came up with a very interesting thought:

The speed of light varies in different materials. In water the value is about 2 x 10^8, apparently. So if this is the case, and chocolate is more dense than water (i think), so we would expect a speed of light in chocolate slightly lower than 2. BUT, we cannot assume that the microwaves remain in the chocolate during their entire traverse through the space inside the microwave. so the value we have measured is some kind of average speed of light during a travel through both chocolate and air.

My colleague also tells me that the refractive index of chocolate is a value often measured in the chocolate industry for quality control...

the things you learn...

thanks to the fellow member who first posted about this... i'm just off to search for your name so i can acknowledge you properly.

EDIT: the member's name was mooeypoo. thanks muchly to you for your idea. it worked beautifully.

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No, I don't think that's it. The standing wave is in the air in the microwave, so the index of the chocolate isn't the problem. Others have recreated the experiment and gotten numbers reasonably close to c.

And the density isn't the only factor in determining the index of refraction. Lightweight lenses for e.g. eyeglasses is a perfect example of lower density/higher index material.

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well the density is a factor, and it allows us to determine roughly what to expect. I used fairly large chunks of chocolate and the wave is definitely inside the chocolate for some of the time, certainly not only in air, or the chocolate wouldn't melt.

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It's moo's video, a good video indeed. I did that myself too. It worked fine to me, of course with some error (round 7.6%)!

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very good video I agree. I still think that we should expect some slowing of the speed of light from the refractive index of chocolate, although yes the larger part of the error is bound to be the imprecision in the frequency of the magnetron.

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well the density is a factor, and it allows us to determine roughly what to expect. I used fairly large chunks of chocolate and the wave is definitely inside the chocolate for some of the time, certainly not only in air, or the chocolate wouldn't melt.

The question, though, is what is the length of the wave that is penetrating the chocolate. Is it the wavelength in the air, or the wavelength in the chocolate? Can a node in the air somehow become something other than a node in the chocolate? I think the key here is that you have a standing wave, not a traveling wave.

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the wave is standing, yes but that doesnt mean the radiation isn't moving, it just means the peaks and troughs remain stationary.

The speed of light varies in different media. If the chocolate melts that must be because at some points the light travels through the chocolate. If light travels through the chocolate it must be slowed down. I don't see how that conclusion can be escaped

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the wave is standing, yes but that doesnt mean the radiation isn't moving, it just means the peaks and troughs remain stationary.

The speed of light varies in different media. If the chocolate melts that must be because at some points the light travels through the chocolate. If light travels through the chocolate it must be slowed down. I don't see how that conclusion can be escaped

If there is a wave in the chocolate, you can't have the peaks and troughs in the same place if you reduce the speed, since the wavelength also changes. I don't think light traveling through the chocolate is the right way to analyze this. You have a field from a standing wave penetrate the chocolate and depositing its energy.

There are a multitude of people who have done this experiment and documented it on the web. All the ones I've seen get close to 3e8 m/s. That's not consistent with measuring a wave in something with a significant change in index of refraction.

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The magnetron is likely to have the right frequency within a pretty tight specification. Assuming you can measure the distance between the melted bits reasonably well I can't see what other explanation for your result is possible apart from the fact that the speed of light is lower in chocolate than air.

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I'd be highly suspicious of the ones posted on the web anyway, since they all knew what the speed of light was supposed to be before they did the experiment and probably wouldnt have posted it unless they felt their results were correct. I wouldn't be at all surprised if many of them re-measured their wavelengths a few times before deciding on a "final" answer.

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why bother with the chocolate? in order to have a standingwave in the microwave you need to have a half integer number of wavelengths along the axis that the waves are traveling on, as the frequency is 2.45ghz and the wavelength is c/f the number of waves will be (n/2) and the length can only be (n/2)c/f=L

2Lf/n=c find n

the best way to find n would be to put a light bulb on the rotating tray of the microwave and look at where it dims/turns off.

warning: you may want to have a beacer full of water in the center to absorb some of the energy, otherwise the metal in the bulb is likely to burn/become a plasma and cause the bulb to explode. Although the the beacer does not guarantee the bulb will not do this.

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the best way to find n would be to put a light bulb on the rotating tray of the microwave and look at where it dims/turns off.

yes thanks for that. Here we see the difference between my definition of "best" and yours. My definition included a consideration of safety and responsibility to my students.

Anyway, if it turned in a circle it'd be moving into and out of the axis of the waves. The wavelength wouldnt be easy to pick up from the pattern derived, i expect.

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the standing wave shouldn't change much inside of the axis, as most microwaves are rectangular, any stray waves should be canceled out relatively quickly with respect to the standing wave.

the experiment is very safe, however I don't know where your students are at, but by all means the experiment is far less dangerous than a number of chem demonstrations i was a party to in high school. (The thermite was a good one)

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When I throw a chocolate bar into my toilet bowl, it usually floats.

But that's just me.

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the standing wave shouldn't change much inside of the axis, as most microwaves are rectangular, any stray waves should be canceled out relatively quickly with respect to the standing wave.

the experiment is very safe, however I don't know where your students are at, but by all means the experiment is far less dangerous than a number of chem demonstrations i was a party to in high school. (The thermite was a good one)

safe as anything. No need for any concern on that, since i didn't use anything they wouldnt have had at home.

I considered doing the thermite reaction but decided it's just too dangerous. Also considered buying some rubidium and decided against it. Next on the list might be a balloon full of hydrogen.

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I'd be careful with the hydrogen as it it tends to make a vary forceful reaction which most people would consider an explosion. especially if its mixed with the oxygen to begin with.

If you have any sort of containment equipment, or if your school would allow a thermite reaction to be done outdoors it would be very safe as well (assuming your not doing it near anything flamable (a baseball field or an empty parking lot ought to do it)

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