# Index of refraction of different wavelengths

1. Dec 13, 2011

### piglet

1. The problem statement, all variables and given/known data

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 ?

2. Relevant equations
2nt=m*lambda 2nt=(m+1/2)*lambda

3. The attempt at a solution
Ive attemped using both wave lengths in the equation doesnt work.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 14, 2011

### 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

3. Dec 14, 2011

### 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

Last edited: Dec 14, 2011