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?
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)λgreen
2nt = mλred
I derived both equations to solve for m and got
2nt/λgreen - 1/2 = 2nt/λred
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.