Polarization by Reflection

fkf

1. The problem statement, all variables and given/known data
Unpolarized light falls on an angle of 37.5 ° with a plan glass surface. The reflected light polarization is examined with a Polaroid. The ratio between maximum and minimum intensity from Polaroid when it is rotated around is 4.0. Which is the refractive of index glass?


2. Relevant equations
I have the Fresnel equations, and the snells law as well. I've also been thinking about malus law.
http://en.wikipedia.org/wiki/Fresnel_equations

3. The attempt at a solution

Since we are given the relationship between max and min intensity with the Polaroid I was thinking that max is when the slit is straight in the direction were the parallel reflected waves go. And min when the Polaroid is in an angle were it lets the perpendicular waves to the incline plane goes. Then it would give a relationship between the parallel and perpendicular reflected waves that are 4.0.

And by this I would try to use the Fresnel equations to solve the refracted angle. And since I'm having the incident angle, refractive index for air and now the refracted angle I would solve the refraction index for glass.

But this somehow doesn't work out. English is not my native language but hopefully you understand me. Thank you.

haruspex

Pls post the details of your working.

fkf

Ok, I will refer to "i" as incident and "r" as reflected. And then "p" as parallel to the incline plane and "s" perpendicular.

Since we have that the max and min intensity has a ratio of 4.0, we have max when the Polaroid slit is 0 degrees from the wave inte the p direction, and min when it's in the s direction. We then have

I_rp / I_rs = 4.0

Since it's unpolarized we also have that I_ip = I _is.

Then I get stucked.

haruspex

In your first post you wrote that you had tried to apply the Fresnel equations but "it didn't work out". That's the working I was wanting to see. Can you work out the angle of the transmitted light? Can you then work out the reflectances for the two polarisations?