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Refraction, Part 2

While Snell was defining his Law of Refraction, many scientists were trying to determine whether light had a finite velocity, and if so, what that velocity might be. It took many years to develop methods and instruments capable of performing such a measurement, and the earliest estimates were of course quite inaccurate.

However, in 1849, H. L. Fizeau came pretty close, with a velocity of about 313,000,000 meters per second (m/s) in air. In 1926, Albert Michelson refined this figure, and also measured the velocity of light in water and in glass. His results were:

Air: 2.9979 x 108 m/s (use 3.00 x 108 m/s)
Water: 2.25 x 108 m/s
Glass: 2.00 x 108 m/s

If we compare the velocity of light in air to that in water, we find that:

C  =  3.00 x 108  = 1.33

VWATER 2.25 x 108

But wait a minute! That value of 1.33 is also the measured index of refraction of water, as determined by Snell in 1621. Snell knew nothing about the velocity of light; he was measuring the observable physical phenomenon. Are the two phenomena related?

In fact, they are directly related. It is because light slows down when it travels through water that we even have the phenomenon of refraction. The relative velocity of light through water (or any other medium) determines the extent to which that light is refracted at the boundary. Thus, we can calculate the index of refraction of any material in either way: by measuring the velocity of light within that material and substituting it for VWATER in the equation above, or by measuring the angles of incidence and refraction and performing Snell's calculation. If both calculations are done correctly, the results will be the same.

For instance, we can calculate the index of refraction of glass from the velocity of light, as above:

C  =  3.00 x 108  = 1.50 = nGLASS

VGLASS 2.00 x 108

Actually, glass may be made with different additives, so the index of refraction of a specific piece of glass may range from 1.50 to 1.60 or so. This can be very useful, as you can see if you look over the section on fiber optics.

More recent tests using modern technology have shown that the velocity of light in air is actually slightly less than in a true vacuum. By definition, nVACUUM = 1.000000. Current measurements show that nAIR = 1.000290 with slight variations due to the fact that air pressure and density vary with the weather.

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