How to measure the speed of light using a microwave

Physics Lab Assignments

Well back in Lab 4, you measured the speed of sound in two different ways. That’s quite an accomplishment because sound travels as fast as a bullet or a jet plane. In this lab, your mission‐ should you decide to accept it‐ is to measure the speed of light! Light‐ about a million times faster than sound. And it may sound crazy, but one way to do that‐to measure the speed of light‐ is to use a microwave safe plate, and uh, marshmallows, or chocolate chips, or a candy car. This one fell over. I’ll just eat. Okay, not the speed of light, exactly, but of microwaves, a cousin of light. Use an ordinary microwave oven, take out the tray inside and the roller mechanism, so it won’t rotate, put the plate of marshmallows or chocolate inside, set it for about thirty seconds or so and let it run. What you’ll see when you take the plate out, is little melted spots in the marshmallows or chocolate. They correspond to the locations of the antinode of the standing wave inside the oven. You want to measure the distance in centimeters between those hot spots as accurately as you can, then follow the directions in Learn. And believe it or not, you’ll be able to calculate the speed of microwaves, and the speed of light! You’ll also see from this of course, why it is that microwave ovens have those turntables to move the food through those antinode hot spots to heat it more evenly. We have a more high‐tech way to measure the speed of light directly, as well, with this equipment. On the left we have a precision, high speed oscilloscope. In the center; a speed of light module kit; on the right side, a spool of 20 meters of fiber optic cable‐ it looks like wire, but it’s actually plastic fiber. Here we have a little light emitting diode that gives off very brief, very rapid pulses of light. If you looked inside the hole, here, you’d see a steady red light because it happens too fast for us to see. The light travels out of here, around and around and around this fiber optic cable‐ 20 meters of cable, a little more than 60 feet of cable, comes back in here, where if you see, by a photo transistor. All this circuitry just runs these two devices here. These wires bring the signals over to the oscilloscope. On the oscilloscope, the top track shows the pulse as being sent out, and the bottom track or graph shows the pulse being received. There will be a picture of this in the instructions on Learn, and from that you’ll be able to measure the time delay between here and here. That’s the time it took for light to travel 20 meters. It’s amazing we can measure something as fast as light going in such a short distance as 20 meters, just amazing!

macaulay.cuny.edu

Kent State University

Act IIILab 8 Lab 8 Measuring the speed of light

The idea: Part 1 of this lab is short and sweet – literally! Part 2 is not bad either.

There is something special about the speed of light. No object can ever travel that fast. Not even an electron, the smallest bit of matter we know, can move that fast; there is not enough energy in the entire universe to make even one electron move at the speed of light. But light can travel that fast, because it is not an object. Light is a phenomenon, electric and magnetic fields tumbling over each other, re-creating each other, through space.

Now when physics folks say ‘light,’ they mean – besides ‘not heavy’ – light that we can see, plus all the relatives of light, other electromagnetic waves. Gamma rays, X-rays, ultraviolet, visible and infrared light, microwaves, and radio waves – they are all the same phenomenon, but of different frequency. And since we know that the medium, not the frequency, determines the speed of a wave, if we can measure the speed of any of those forms, we know the speed of all of them.

Your microwave oven creates electromagnetic waves of a known frequency. In Part 1 of this lab you will measure their wavelength, and can then easily calculate their speed. In Part 2 you will measure the speed of visible light, using data from an electronic apparatus, and an oscilloscope stretched to its limit. Let’s go!

What you’ll learn: By the end of this you will understand why most microwave ovens have rotating turntables. More related to this course, you will learn 1) how to measure the wavelength of a microwave, 2) two ways to calculate the speed and expected speed of light, and 3) how to do calculations involving index of refraction.

8.1

What you’ll need: Microwave oven Small metric ruler

Calculator Microwave-safe glass dish or paper plate Miniature marshmallows or chocolate chips or a large chocolate bar Image of an oscilloscope screen

What you’ll do: Part 1

1) Remove the turntable and the bearing ring from your microwave oven. See if you can find a shallow, rectangular glass dish that fits nicely in the microwave oven. If not, a paper or foam plate will do.

2) Line the dish with marshmallows standing on their ends, one layer thick. Or tile over the paper plate with marshmallows standing on end. Or, spread a thin layer of chocolate chips over a paper or foam plate, or, unwrap a large chocolate bar and place it on a paper plate.

Whatever you chose to use, place it in the microwave oven and heat for a few seconds at a time until you see the marshmallows or chocolate start to soften or melt in certain hot spots. Don’t heat too long, or the hot spots will grow and become difficult to measure.

3) Remove the dish or plate from the oven and carefully measure from the center of one hot spot to the center of the next, in cm. You may you need to make several measurements and average them out. Or you may decide to eat the marshmallows or the chocolate and start over. That’s fine with me. But seriously, record the distance between the hot spots on the Report Sheet.

4) The hot spots appear at the antinodes of the standing wave that forms inside the oven. As with any standing wave, the distance between two successive antinodes is one-half wavelength. Double the measurement from Step 3, convert it to meters, and record that measure of the wavelength on the Report Sheet. You are almost done already!

5) Look up on the internet the frequency of the microwaves produced in microwave ovens. You may find the answer in terms of Gigahertz (billions of hertz) or Megahertz (millions of hertz). Whichever you found, multiply by a billion or a million, respectively, to convert the frequency to Hz and record that number.

8.2

6) Finally, multiply the frequency from Step 5 times the wavelength from Step 4. Round to two digits and the correct number of zeroes and record it in the table on the Report Sheet.

Technically, we have measured the speed of microwaves, and therefore light, through air. The value is only three-hundredths of a percent lower than the speed of light in a vacuum, and that is well within the range of experimental error, so we can ignore the difference.

Part 2

In this part of the lab you will measure the speed of light rather passively, I’m afraid, as this lab is not conducive to controlling by remote access, as you did in Labs 3 and 7.

In Smith Hall we have electronic kits that produce a series of extremely short pulses of laser light from the blue upper connector on the right side. They travel through a 20.0 m long piece of fiber optic cable, and are received by a detector in the lower black connector on the right side. A high speed oscilloscope monitors both the outgoing and incoming signals through those two long black connectors that you see in the photo.

∫ to a 20 m long spool of fiber optic cableª back from the spool of cable

8.3

The upper channel trace on the oscilloscope screen below displays a frog-on-a-post graph of the light pulses as they are emitted, and the lower line on the oscilloscope shows the pulses as they are received.

If light traveled infinitely fast, the peaks in the two traces would line up. But even though the speed of light is the fastest known speed in the universe, it is not infinite! Light takes a tiny bit of time to travel any distance, even 20 meters.

As a result, the lower trace on the screen is shifted a little to the right. The difference in the position of the two peaks tells the time for light to travel

20.0 m.

7) Open and print the enlarged image of the oscilloscope screen, in the same item as these instructions. Use the time scale information on that page, and as carefully as you possibly can, estimate the time delay caused by passing the light through the cable. Record that time, in seconds, on the Report Sheet.

8) Calculate the speed of light in the plastic cable, knowing that it traveled 20.0 m in the time you just found in step 8.

9) There is just one complication. Light travels more slowly in any material, such as the plastic in this cable, than in a vacuum. The speed of light in some substance is related to the speed of light in a vacuum, c, by this expression:

n = speed of light in vacuum/speed of light in some material n = c/v

where v is the speed of light in a material and n is called the index of refraction of the that material. Think of n as the slowing-down factor, or how strongly light is bothered or pestered by the medium – how much light is affected by it.

The manufacturer of the fiber optic cable reports that the value of n for their cables is 1.25. Use that value along with your measurement of the speed of light in the cable to estimate the speed of light in a vacuum, c, and record it.

8.4

10) You know from the companion class that the speed of light, to two decimal places, is 3.00 x 108 m/s, or 300,000,000 m/s. Calculate the percent difference between each of your estimates for the speed of light, from Parts 1 and 2, and that known speed. Enter those percent differences on the Report Sheet

Web extension

One of the best measurements ever made of the speed of light was accomplished by Albert Michelson and E. W. Morley at what is now Case Western Reserve University in Cleveland. Find out what year they made that measurement, and the value they found for the speed of light.

Be sure to include the web address of the site where you found the information.

8.5

Kent State University Act IIILab 8

Measuring the speed of lightReport sheet

Name Objective: To 1) measure the wavelength of a microwave, 2) calculate the speed of light in two ways, and3) perform calculations involving index of refraction.Data: Part 1 Distance between hot spots,cmWavelength of microwave,cmWavelength of microwave,m Frequency of microwaves,Ghz or MhzFrequency of microwaves,HzSpeed of microwaves andspeed of light, m/s

Part 2 Number of small ticksbetween peaksTime between peaks, s Speed of light in the fiberoptic plastic, m/sSpeed of light in vacuum,m/sPercent difference fromknown speed, Part 1Percent difference fromknown speed, Part 2

Comment on why either method (Part 1 or Part 2) may be more accurate.

Web extensionWhen did Michelson and Morley, in Cleveland, make their precisemeasurement of the speed of light? What did they measure for its speed?What source did you consult for your answers?

PR Photo (Proof you Really did the experiment)Upload a photo of you with the melted marshmallows or chocolate.