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# Speed of Light

by Ron Kurtus (revised 6 October 2007)

The speed or velocity of light is approximately 186,000 miles per second or 300,000 kilometers per second in a vacuum.

All electromagnetic waves, including visible light, travel at that speed. With such an enormous speed, it has been difficult to devise experiments to measure it. The speed of the electromagnetic waves slows down when they pass through matter.

According to the Theory of Relativity, the speed of light is the fastest at which anything can travel.

Questions you may have include:

• How is the speed of light measured?
• What is this speed's relationship to matter?
• Can things go faster than light?

This lesson will answer those questions. Useful tool: Units Conversion

## Measuring the speed of light

Since the speed of light is so great, it is very difficult to measure.

Note that the terms speed of light and velocity of light are used. Either one is acceptable, but you must remember that speed means how fast something is going, while velocity means how fast it is going in a given direction.

### Echo method not practical

It was thought that the velocity of light could be measured that same way as for the velocity of sound. A common method to measure the velocity of sound is to calculate the time it takes for an echo to return and then divide that by the distance the sound travels there and back. Since distance equals velocity times time:

c = d/t

where

• c is the speed of light (light's speed is always denoted as c)
• d is the distance traveled
• t is the time it takes to go that distance
• d/t is d divided by t

But the velocity of light is so large at 186,000 miles/sec (300,000 km/sec), that in 1/1000 of a second, the light would travel from Milwaukee to Chicago and back (or from Los Angeles to San Diego and back). That is over 90 miles (150 km) one way.

If you used a timer or shutter that could measure in 1/100,000 of a second, it might be be more practical.

### Spinning pinhole

One clever method that was one of the first to measure the speed of light was to shine a light through pinhole on a spinning disk. The light was then reflected off a mirror that was some distance away.

Since light travels so fast, it would normally be reflected back through the pinhole (provided everything was lined up properly). By adjusting the speed of the spinning disk and/or the distance, the pinhole could be made to move enough that the light would not pass through it. Then, by calculating the size of the pinhole, the speed of the disk, and the distance to the mirror, the speed of light could be calculated.

### Modern methods

With modern electronics, the speed of light can now be measured in a physics lab.

One example to measure the speed of red light is to use equipment that includes a LED (light-emitting diode) that emits a regular series of pulses of red light that are only 20 nanoseconds in duration.

(A nanosecond is one-billionth of a second or 1/1,000,000,000 second. It is also written as 10-9 seconds, 10^-9 or 1e-9, where the -9 indicates the number of zeros in the denominator.)

That means the pulse of light blinks on for 20 billionths of a second or 20/1,000,000,000 second and blinks 40,000 times per second. Having such a short pulse allows the scientist to measure the difference in time it takes to travel two different paths. If the duration was longer, the distance traveled would have to be longer.

By splitting the light beam with a half-silvered mirror, one beam travels to a mirror 10 meters away and then back to a photodiode detector. The other beam is reflected off a mirror only a few centimeters away. The time difference for the two beams is about 67 nanoseconds, which can be displayed on a regular dual beam oscilloscope.

The total distance the light travels is 20 meters, which equals 0.02 kilometer (20/1000).

The speed of light is then:

c = 0.02 kilometers/67*10-9 seconds = 298,500 kilometers per second

This is a fairly accurate reading and pretty close to the actual speed of 299,792 km/s.

## Speed through matter

The speed of electromagnetic waves passing through transparent matter is slower than it is in a vacuum. Glass is transparent to visible light, radio waves will easily pass through non-metals, and x-rays pass through most materials except lead.

Most measurements of the speed of light are made in the atmosphere. Since the effect on the speed when passing through air is so very small, the speed of light in air is almost the same as it is in a vacuum. The difference is negligible.

The reason electromagnetic waves travel slower though transparent materials is the effect that the electrons have on the waves. They act somewhat like a "friction" on the waves.

### Light through glass

The fact that light moves slower through matter can be seen when visible light passes through glass. If you shine a light at an angle through a piece of glass, the light beam will be bent or refracted.

(See Refraction of Light for more information.)

The ratio of the speed of light in vacuum divided by the speed of light in the material is called the index of refraction for the material. The index of refraction of glass or other material indicates how much slower the light travels through the material than in a vacuum.

Typically, the index of refraction of glass is from 1.2 to 1.5. That means the speed in a material of index 1.5 is 66% of the speed in vacuum.

### Extreme slowing

Although the speed of an electromagnetic wave through matter is can be up to 50% less than the speed through a vacuum, scientists were able to greatly reduce the speed through matter in special situations. This was first done in 1999.

Danish physicists performed an experiment where they slowed light down to only 38 miles per hour or about 57 kilometers per hour. They did this by sending a beam through a material made of sodium atoms cooled to near absolute zero (-273°C or -460°F). They achieved this low temperature by using lasers to slow down the atoms, through a special method used in quantum mechanics called the Bose-Einstein condensate. (Explanation of this goes away beyond the scope of this course).

## Speed is the maximum

The speed of light is supposed to be the maximum speed at which matter can travel.

### Matter changes

In fact, according to Einstein's Theory of Relativity, strange things happen to matter as it approaches the speed of light. Matter becomes compressed as it gets within 90% of the speed of light, such that a ruler would appear shortened. Also, the mass of the matter starts to increase.

### Time changes

Another interesting phenomenon happens when matter approaches the speed of light, and that is that time for the matter slows down. In other words, if you were traveling through space near the speed of light, you would age more slowly than a person on Earth. A year year trip might seem like 10 minutes to you, while it would seem like a full year to everyone else.

Time travel or going at "warp speed" as is seen in such TV shows as Star Trek is not physically possible, as far as we know.

## Summary

The speed of light is approximately 186,000 miles per second or 300,000 kilometers per second in a vacuum. All electromagnetic waves, including visible light, travel at that speed. Modern electronics allow the measurement of the speed of light in a physics lab. Light and other electromagnetic waves slow down when they pass through matter. According to the Theory of Relativity, the speed of light is the fastest at which anything can travel. The speed of light is the maximum speed for matter.

Get your work done quickly

## Resources and references

Ron Kurtus' Credentials

### Websites

Physics Resources

### Books

Schaum's Outline of Optics by Eugene Hecht; McGraw-Hill (1974) \$16.95

Introduction to Modern Optics by Grant R. Fowles; Dover Publications (1989) \$16.95

Optics by Eugene Hecht; Addison Wesley (2001) \$108.00 - Textbook covers wave motion, electromagnetic theory, propagation of light, optics, lasers and other advanced aspects of light

## Questions and comments

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