The wavelength and frequency of light in a medium obeys the relation
where v is the speed of light in the material and is equal to c/n, where n is the index of refraction of the material. Since the frequency of the radiation does not change, we end up with a wavelength ln that depends on the material in which the light is propagating.
This is the wavelength that must be used in thin film and coating situations. It leads to the concept of optical path length. Two paths may have the same physical length, but contain a different number of wavelengths. The optical path length of a path of length L is just Ln.
Suppose two rays with 450 nm wavelength travel 4.5 cm. in tubes. One tube is filled with a low density gas and the other is evacuated. n=1 for vacuum and n=1.000005 for the gas. What is the optical path length difference in nm between the two paths?
vacuum optical path length = Ln = 4.5·10-2(1.00)
gas optical path length = Ln = 4.5·10-2(1.000005)
the difference between the two is 2.25·10-7 = 225 nm = l /2. The two rays will destructively interfere.
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