Question

A transparent oil with index of refraction n = 1.24 spills on the surface of certain crystal (with unknown
index of refraction) with a thickness of 0.423 μm. Normally incident red light (wavelength 700 nm in air)
produces a maximum of reflection.
(a) What can you tell about the index of diffraction of the crystal?
(b) Which wavelength in the visible spectrum (400 nm - 700 nm) would also give constructive interference?
And destructive?
(c) Which index of refraction should your crystal have to change the interference pattern observed?

Answer 1

(a) For interefernce to happen, the index of refraction of the crystal should be more than the index of refraction of oil.
n crystal > n oil (1.24)

(b)

The formula to apply for find the maximum for this thin film is

2nt = mλ

(2)(1.24)0.423*10^-6 = (1)(lambda)

lambda = 1049 nm (no)
lmabda = 1049/2 = 524.5 nm (yes)

2nt = (m-0.5)λ

(2)(1.24)0.423*10^-6 = (0.5)(lambda)

lambda = 2098 nm (no)
lmabda = 2098/3 = 699 nm (yes)
lambda = 2098/5 = 419.6 nm (yes)

(c) n crystal < n oil (1.24)