How To Calculate The Speed Of Light In Your Kitchen Content from the guide to life, the universe and everything

How To Calculate The Speed Of Light In Your Kitchen

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A kitchen provides ideal conditions for calculating the speed of light in.

The speed of light is, as everyone knows, 186,000 miles per second or 299,792km per second. That's pretty fast. However, that's the speed when light travels in a vacuum; in air, it slows down to 299,552km per second which doesn't sound quite as fast. A London bus travelling at the speed of light could travel from London to New York and back twenty five times in one second. But, how could you prove that? And how could you prove that in your kitchen? For this experiment you will need:

  • A microwave oven
  • A plate
  • Some cheese
  • A cheese grater
  • A ruler

Please ask an adult to help, as microwave ovens can be dangerous.

Grate enough cheese to cover the plate to a depth of about 5mm. Take the glass turntable and any roller mechanism out of the microwave and put the plate of cheese in. Turn the heat to full power for 20 seconds. When you take the plate out, you will see two lines of melted cheese.

The reason for this is the oven has a microwave emitter in the side which sends out energy as a wave - the same sort of wave as a radio wave or a light wave. This wave is perfectly even and regular. Imagine a line on a graph that curves up to a peak then down to a trough. Where the wave is at its highest and lowest points, it is reinforced by the waves that are bouncing around inside the oven so that two hot spots are created a half-wavelength apart.

Most microwaves have a stationary emitter and the food is revolved on a turntable to rotate it evenly through the hotspots. This is why it is impossible to microwave an ant. If you put an ant into a microwave and watch through the window when you switch it on, you will see the ant scurrying around on the turntable. Whenever the table rotates through a hot spot, the ant simply runs away from the heat to a cooler area. Some microwave ovens have a rotating emitter. The plate in these ovens stands still and the hot spots move. If your microwave doesn't have a turntable, it won't be possible to do this experiment unless you can train some ants to carry the plate on their backs and run at a constant speed in front of the hotspots.

Where the cheese has melted is where the wave was at its highest and lowest spots. Wavelength is the distance between two peaks so by measuring the distance between these two lines of melted cheese we can find half the wavelength.

It may be difficult to find the exact centre of the lines in the melted cheese, but try to be as exact as you can. In the h2g2 kitchen, the distance was found to be 60mm. Multiplying this by 2 gives us the wavelength: in this case, 120mm.

We now know how long the wave was, but we need to know how many waves there are per second. On the back of the oven will be a label that tells you the frequency the oven operates at. On the h2g2 microwave it was 2450MHz, or 2450 million waves per second.

So, 2,450,000,000 cycles per second
120mm = 0.00012km
In 1 second, the wave travels 2,450,000,000 x 0.00012km = 294,000km

This tells us that the speed of light is 294,000km per second: quite close to the actual figure of 299,552km per second, within 2% anyway. When you consider how difficult it was to measure the lines of melted cheese, this is pretty much spot on.

Congratulations. You have just calculated the speed of light in your kitchen1.

Now wash your hands.

1To calculate the speed of light in other rooms, you will need to move the microwave.

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