# The Speed of Light in Your Kitchen Visiting the Local Hot Spots

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### The Idea

Light is an electromagnetic wave. Because of its extremely high speed, it is difficult to measure the speed of light directly. Historically, astronomers such as O. Roemer used distances on the scale of planetary orbits to get a handle on how fast light traveled through space. In this project, you measure the speed of light right in your own kitchen. The technique is similar in principle to the approach we used in Project 73 where we found the speed of sound by finding its resonant wavelength. Here, you use a microwave oven to establish a standing wave that can be used to estimate the speed of light.

### What You Need

• microwave oven
• sheets of sliced cheese, bars of chocolate, or about five eggs
• sheet or plate to hold above food items without rotating in the oven—some ideas include a rectangular wood or plastic cutting board, a rectangular Pyrex baking dish, a round dish that fits as close wall-to-wall as possible, or a sheet of poster board cut to size. Obviously, remember no metal should go in the microwave oven.
• ruler
• calculator
• light, so you can see inside the oven (the oven may have an adequate light built in)

### Method

1. Microwave ovens rotate to spread out the hotspots in the oven. In this experiment, we want to detect these hot spots. So, if your microwave oven has a rotating tray, remove it from your microwave oven.
2. Put a nonrotating sheet or plate in the bottom of the microwave oven.
3. Cover the plate with the microwavable food: cheese slices or chocolate slabs. The layer should be as uniform as possible in thickness and composition. If you choose to use egg whites, pour a thin layer into a suitable dish and spread it out to form a thin, uniform layer.
4. Look through the glass window of the microwave oven and start the microwave oven on the lowest available power setting. Use a light shining from outside if that helps you observe what is going on inside the oven. If you don't have a window, you need to cook in increments. Because microwaves differ so much in power, you need to determine an appropriate amount of time to use for this: 10 to 15 seconds is a good place to start.
5. Continue running the microwave oven until you notice the first signs of melt spots or cooking.
6. Stop the microwave oven and identify the pattern of melt spots. Unless you are sure the microwave oven has run long enough to establish a clear melt spot pattern, do not move the tray in the oven yet.
7. Measure the center-to-center distance between adjacent melts spots. An example for what you are looking for is shown in Figure 84-1.
8. Because one-half of a wavelength fits between each hot spot, the wavelengths for the microwaves in the oven are twice the center-to-center distance measured.
9. Look for a label or search online for the specific microwave frequency used in your microwave oven. If you cannot easily find this frequency, you can use 2450 MHz, which is the frequency at which most commercial microwave ovens operate.
10. When you finish, you can make grilled cheese sandwiches, s'mores, or egg-white omelets with the leftover food ingredients.
11. Calculate the speed of light using the equation:
12. c = λf

or speed of light = the wavelength/frequency

For λ use the wavelength (in meters) from twice the center-to-center hot spot distance.

For f, use 2450 MHz, which is 2,450,000,000 Hz or 2.45 × 109 Hz (unless otherwise indicated on the microwave oven).

### Expected Results

Suppose you find the average of the hot-spot distance is 6 cm.

The wavelength of the microwave resonant in the microwave oven is 12 cm.

In meters, this is 12 cm × 0.01 m/cm × 0.12 m.

The speed of light is then, c = 0.12m × 2,450,000,000Hz = 2.94 × 108 m/s.

This is reasonably close to the accepted value, which is just under 3 × 108 m/s (300,000,000 m/s). Remember, microwaves may vary in how they create standing waves and an error factor is associated with heat distribution on the heat surface. For this reason, this measurement can be only expected to give ballpark, not precisely accurate, values.

### Why It Works

A microwave oven produces a resonant wave in the oven chamber similar to that of a vibrating guitar string. The hot spots are like the nodes or the points where the ends of the string are held. A complete wave is a cycle up and down, so only a half wave fits between the two nodes in both cases. From knowing the frequency of the microwaves and measuring its wavelength, we can find the speed of light.

### Other Things to Try

A more sophisticated, but more precise way to measure the speed of light is to detect the interference between light waves separated by a measurable distance. Equipment to do this is available from scientific supply vendors, such as PASCO.

### The Point

The speed of a wave, such as light, can be determined from its wavelength and frequency. The wavelength of a microwave oven can be found by the distance between the nodes of a resonant standing wave.