While a single-layer coating on the surface of a glass lens can reduce the refle

Question

While a single-layer coating on the surface of a glass lens can reduce the reflection of a particular wavelength of light using thin-film interference, multiple coatings of materials with different indices of refraction reduce the reflection of more than one wavelength. A given glass lens (n = 1.52) is coated with a material that has an index of refraction of 1.65 (CeF3) over which is a top layer with index of refraction 1.38 (MgF2). Find the film thickness of the top layer (MgF2) if reflections of wavelength = 555 nm will be minimized.

Explanation / Answer

Hi,

In this case we have a multi-layer anti-reflection coating which uses the thin-film interference to produce destructive interferences that can greatly reduce the effect of the reflection.

The ideal thickness for the layers in this case is a quarter of the wavelength we want to minimize. Therefore, the thikness of the top layer in this case is equal to:

t = /4 = 555 nm/4 :::::::::::::::::::::::::: t = 138.8 nm

If we had had a multi-layer with three materials: MgF2 at the top, CeF3 at the bottom and some other material with a higher index of refrection than the other two (for instance, ZrO2) in the middle, the optimum thickness of each layer would have been /4 for the MgF2 and CeF3 and /2 for the third material.

I hope it helps.

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