# Polarization Question

1. Apr 26, 2006

### BobbyBobbyBob

A thine file of ethyl alcohol (n=1.36) is spread on a flat glass plate and illuminated with white light. When illuminated and viewd from directly above, it shows a coloured pattern in reflection. If the only visible light reflected by a certain region of the film is yellow (lambda=560nm), how thick is the film there? Justify (assume visible spectrum is 400-7800nm)

I have no idea where/how to start and what it involves.

I have a feeling it invovles Huygen's Principle and Polarization by Reflection.

2. Apr 26, 2006

### Andrew Mason

I think this is about thin film interference. There are two surfaces that are reflecting light: the air/alcohol surface and the alcohol glass surface. I think you are supposed to assume that the index of refraction (n) of the glass is greater than 1.36.

AM

3. Apr 27, 2006

### marlon

This is a thin film interference problem. The index of refraction of glass will indeed exceed the 1.36 value.

If you look at the theory behind this thin film interference. I assume you know the formula's that express the destructive and constructive interference. Generally, you just apply these formula's to the reflected beams on one specific side of the film.

The clue is, however, that you need to know the relative magnitude of the refraction indices of the media that are separated by the film. Mostly there are three media (one on the left, one inside the film and one on the right). If a wave reflects on a medium of which the refraction index is BIGGER then that of the medium in which the wave is propagating, there will be a phase change of 0.5 times the wavelength. One can prove this, using the Fresnel relations.

You will need to determine at which plane of the film, this phase change will arise. If it arises at only one of the two planes then the reflected waves will have a phase difference of 0.5 times the wavelength wtr to each other. The formula for destructive interference now expresses the actual constructive interference because of this relative phase change.

regards
marlon