# Homework Help: Degree of Polarization

1. Oct 10, 2005

### TimNguyen

A beam of natural light is incident (from the air) on an air-glass interface at 40 degrees. Take n = 1.5 for the glass.

a)Obtain an expression for the degree of polarization of the transmitted light and compute it numerically.

b)Obtain an expression for the degree of polarization of the reflected light and compute it numerically.

c)Obtain an expression for the degree of polarization of the transmitted light when the angle of incidence is Brewster's angle and evaluate it numerically.

The only formula that I'm given is that the degree of polarization is equal to I(polarized) / [I(polarized) + I(unpolarized)].

How do I know which light is polarized and obtain the intensity for each polarized/unpolarized light?

2. Oct 11, 2005

### TimNguyen

Could anyone help out?

3. Oct 11, 2005

### CarlB

It might help if you mentioned what kind of class you're taking and what sort of other things you've been studying.

I'm going to guess that you're taking a class where you're discussing the electric and magnetic fields associated with light.

The problem amounts to determining the boundary conditions between E&M in air and E&M in glass. The solution is that the tangential E&M fields are continuous and that this is enough to define the changes in angles.

You will have to work it out twice, once with light polarized one way and once with light polarized the other. That is, one way the E field is tangential to the surface, the other way the B field is tangential.

After you get the transmission and reflection coefficients for the two ways light can arrive, you will see that there is a difference in how much they reflect and transmit. That makes the light that is reflected polarized even if the light coming in wasn't. That's what you're calculating.

Good luck, it's a tough assignment.

Carl

4. Oct 11, 2005

### vanesch

Staff Emeritus

You must have had something that's called "reflexion and transmission at planar interfaces", no ?
Look for something called "Fresnel relations" which give you the relative intensities of reflected and transmitted light incident under an angle for the two polarizations (perpendicular and parallel to the reflecting surface).

As CarlB suggests, consider the incident light as a 50-50 mix of both, and then see what fraction survives after reflexion or transmission and how much it deviates from this 50-50 ratio in both cases.

cheers,
Patrick.