Index of refraction of different wavelengths

[piglet]

Homework Statement

Monochromatic light of variable wavelength is incident normally on a thin sheet of plastic film in air. The reflected light is a maximum only for 482.9 and 676.0 in the visible spectrum. What is the minimum thickness of the film ?

Homework Equations

2nt=m*lambda 2nt=(m+1/2)*lambda

The Attempt at a Solution

Ive attemped using both wave lengths in the equation doesn't work.

Answer is 525nm.

 

[technician]

This effect is caused by interference between light reflected from the front surface of the film (the air/film surface) and the back surface of the film (film/air surface)
The first reflection introduces a phase shift of pi.
The light passing into the film introduces a path difference.
Hope this shows you how to proceed

 

[ehild]

The order of interference (m) for both wavelengths differ by 1. But you can not get the thickness without the refractive index. Is it n=1.61?

The reflected light is maximum if

2tn=(m+1/2)λ,and this is true for two wavelengths =>
(m₁+1/2)=(2tn)/λ₁
(m₂+1/2)=(2tn)/λ₂

Subtracting the equations we get that 2tn(1/λ₁-1/λ₂)=1. Solve for t.

ehild