Measuring Speed of Light with a bar of Chocolate!

How anyone can easily measure the speed of light from the comfort of their kitchen.

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In case you were wondering, yes, it is possible to calculate the speed of light from the comfort of your kitchen! This is a relatively famous experiment that is often performed while doing Physics A-levels or GCSES. All you need is a big bar of chocolate (the bigger the better), a centimetre ruler, and a microwave oven.

To be able to do this experiment and calculate the value of speed of light, we will be revising some very basic math formulas. All you need to know are some fundamentals of algebra such as multiplications and rearrangement of simple brackets.

Anyone who has done science at high school would be aware with the equation:

I will be using the letters ‘V’ for speed, ‘S’ for distance, and ‘T’ for time. If you know any of the two variables, you can work out the third one; if you know the distance a car has moved and the time it took to cover that distance, then you can calculate its speed.

To understand the experiment and how it works, we need some knowledge about waves. When physicists use the word ‘light’, they often refer to the whole electromagnetic spectrum, which includes waves of different wavelengths (length of a wave) from the very large radio waves to the very small gamma rays. It is possible to calculate the speed of a wave the same way as you would calculate the speed of a car.

The equation for speed of light looks a bit different because you introduce a new variable named frequency, which can be defined in relation to time period. Time period is the number of seconds it takes for one wave to pass through a given point. Frequency is how many waves can pass through a point in a given second. Hence frequency can be written as ‘1/T’ or inverse of time period. Following from our very first equation, the equation for speed can be written as:

Since we know that 1/T is frequency, denoted by ‘f’, the equation can be re-written as:

When talking about waves, the distance between two consecutive troughs, or crests is referred to as one wavelength. However, we have different letters to denote each variable when it comes to waves, for example ‘c’ for speed and ‘λ’ (lambda) for wavelength. Hence we can write the equation as:

Another thing we need to be familiar with is the concept of standing waves. This is what a standing wave looks like:

If you look carefully, you will observe that at some parts the wave is stationary and at other parts it is moving up and down. The stationary parts are called nodes, and the points where the extreme positions can be observed both upside and downside are called anti nodes. Anti-nodes are the points where the amplitude of the wave is the highest or where it has the most vibration. For the visual aid, you might want to take a look at the following figure:

So far so good, now we will learn a little about harmonics. The distance between node to node or between anti-node to anti-node is half of the wavelength and is called the first harmonic. Hence we can say,

The picture above is the first harmonic and as you can see, it is half of a wave, not a complete wave, therefore length between the nodes is half of the wavelength.

Therefore, if you are given the length, you can work out the λ by multiplying the length by 2.

If you have kept up with the article so far, then you should be able to follow the logic of what comes next. One thing you have to remember is that microwaves are a part of the electromagnetic spectrum; if you read the label on your microwave, it will tell you the frequency of the microwaves in your oven. They will be given in MHz (Mega Hertz) and you need to convert it into Hertz by multiplying the frequency with 106(or by multiplying by 1000000), if it is given in GHz, then multiply by 109.

Our experiment is ready to be performed. Take the rotating plate out of the microwave and place the chocolate bar on a household plate (the flatter the better) and then insert it back into the microwave. Let it run on low power for about 30-45 seconds and make sure the chocolate is only slightly melted rather than getting fully melted. When the chocolate is heated, hot spots will appear on it, indicating the concentration of microwaves. These hot spots represent anti-nodes. Use a cm ruler to measure the distance between two anti-nodes and once you have calculated the length, you have to convert it into meters by multiplying that length by 10-2 (or dividing by 100). Following the first harmonic, we know that length is λ/2, therefore, to find λ, you need to multiply length by 2. This will give the value of the wavelength.

After the wavelength has been calculated and frequency jotted down, speed of light can be easily worked out. The frequency-wavelength equation (c=f λ) will give you the speed of the wave in meters per second, and hence the speed of light!

Due to uncertainty that may be present because of systematic and random errors, you will not get the exact true value, but compared with the actual value: 299,792,458 m/s, the answer will be pretty close.

Congratulations, you just calculated the value of speed of light, even more accurate than Galileo’s first calculated value. Go on and have some of that partially melted chocolate, you deserve it!

Abdul holds a BSc (Hons) in Theoretical Physics from Swansea University and is currently a Postgraduate student in Cosmology, at the University of Sussex. Outside of Cosmology, he is interested in Philosophy in general and Philosophy of physics and religion in particular.
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