# Measure the speed of light

## Objectives

After working through this chapter, you should be able to:

• Explain how microwaves heat food using interference

• Explain how we can use chocolate to measure the speed of light

## Introduction

In chapter 1 we briefly mentioned different types of electromagnetic radiation, one of which involved a type of energy you can find in most kitchens – microwaves . As a quick recap, microwaves are a form of electromagnetic energy comprising wavelengths that fall between infrared and radio waves, meaning that in general terms their wavelengths are relatively long, and they exert relatively low energy compared to other types of energy (e.g. UV) ( Fig. 21.1 ).

Now, it’s probably no surprise to hear that one of the most easy-to-understand practical uses of microwave radiation is for the generation of heat (thermal energy) in a microwave oven. This means that every time you convert an item of food from a chilled substance into its molten lava counterpart in the microwave, you’re technically doing a scientific experiment that utilises interference properties of electromagnetic radiation (see chapter 10 ). This is possible because the microwave energy is absorbed by fats, sugars, proteins and water, causing them to heat up. The microwaves also interfere with each other causing the formation of hot spots in the food in locations where constructive interference takes place. This can be likened to the ‘bright maxima’ we discussed in chapter 10 , but instead of bright light, it produces hot spots. If your microwave contains a turntable, then the turntable serves to dissipate these hot spots, enabling food to be cooked more evenly, and if your microwave doesn’t contain a turntable, then instead it will contain a built-in, rotating motor which serves the same purpose.

The hot spots generated by the constructive interference are related to the wavelength of the microwaves, as anywhere two peaks or two troughs align, there will be maximum heat produced ( Fig. 21.2 ). This means that the distance between the hot spots will equate to half of the wavelength.

## The experiment

In order to find the wavelength of the microwaves in our microwave ovens, we purposely want to create hot spots within the oven – thereby cooking something incredibly unevenly. . . . This means we will need to remove the turntable from the microwave before we begin.

Please note: if your microwave does not contain a turntable (or if the turntable can’t be removed), then unfortunately you won’t be able to do this experiment unless you borrow someone else’s microwave.

## Notes of caution

• Microwaves produce heat. Be careful not to burn yourself, particularly as the turntable used to distribute the heat is not being used.

• Do not place metal objects in the microwave oven. Microwaves reflect off metal and will damage the internal workings of the microwave oven.

• Do not use the microwave without food inside; if there is nowhere for the microwaves to go, they will damage the microwave oven.

## Equipment required

• Microwave oven that utilises a removable turntable

• A 10 cm+ bar of chocolate (select one that’s tasty and then you can eat it afterwards)

• A timer

• A ruler

## Method

• 1.

Prepare the chocolate to be as flat as possible (e.g. grating the bumps off the chocolate).

• 2.

Read the frequency ( ν ) of the microwave off the label on the back of the microwave oven or by consulting the manual, and make a note of it somewhere . It is usually given in megahertz (MHz), which must be converted to hertz (Hz). Convert from MHz to Hz by multiplying by 10 6 (e.g. 2,450 MHz = 2,450,000,000 Hz).

• 3.

Remove the turntable from the microwave oven.

• 4.

Place the prepared chocolate onto a microwave-proof tray and then place in the microwave .

• 5.

Microwave the chocolate in short, 5-second bursts and examine the food after each burst. You are looking for the point at which the chocolate just begins to melt. Two (or more) areas of melting will occur.

• 6.

Once visible, measure the distance between the two hot spots with a ruler . Convert this measurement into metres and multiply by 2 to get the wavelength (λ).

• 7.

Calculate the speed of light using the equation below:

speed of light = wavelength × frequency