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## Homework Statement

You are working with the mineral fluorite (CaF2, n=1.43) and have a sample that is coated with a layer of liquid 158 nm thick. For various wavelengths of visible light incident normal to the surface of the liquid, you observe very strong reflection for green light (λ = 510 nm), essentially zero reflection for red light (λ = 750 nm), and intermediate levels of reflection for all wavelengths between the red and green extremes. What is the index of refraction of the liquid?

## Homework Equations

2nt = mλ

2nt = (m+1/2)λ

## The Attempt at a Solution

The index of refraction of the liquid can either be greater or smaller than that of mineral fluorite.

First I assumed the first case was true. Because only one phase shift occurred, the constructive condition for green light and destructive condition for red light respectively are:

2nt = (m+1/2)λ

_{green}

2nt = mλ

_{red}

I derived both equations to solve for m and got

2nt/λ

_{green}- 1/2 = 2nt/λ

_{red}

And solving this gave me n = 2.52

I did the same thing with second case which gave me n = -2.52.

However my answer is incorrect. Can someone please point out what I did wrong?

Thanks a lot.