What is the thinnest film of a coating with n = 1.42 on glass (n = 1.52) for whi

Question

What is the thinnest film of a coating with n = 1.42 on glass (n = 1.52) for which destructive interference of the red component (wavelength = 650 nm) of an incident white light beam in air can take place by reflection? [Hint: consider the light that will be reflected off the top and bottom of the coating and refract back into the air. In the coating, the light will be travelling slower, so its wavelength will change by: wavelength = wavelength original/n. What will be the relative phase shit between the two reflected light rays?]

Explanation / Answer

The formula for destructive interference in this case is,

2nt = (m + 0.5)(wavelength)

(2)(1.42)(t) = (0.5)(650 X 10-9)

                t = 1.14 X 10-7 m

                  = 114 nm

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