Finding refractive index from polarized reflection intensity ratio

[Sheepwall]

Homework Statement

Unpolarized light hits a flat glass surface, 37.5 degrees to the surface's normal. The reflected light's polarization is investigated with a polaroid. The relationship between the max and min value of intensity from the polaroid when it is rotated is 4.0. What is the index of refraction of the glass?

Homework Equations

Fresnel's equations and Shell's law.

The Attempt at a Solution

I have got no clue, and I've gotten rather frustrated. The only thought I have is that the reflected polarized intensity is 1.5 times that of the non-polarized reflected intensity. Please aid me, I do not enjoy this part of physics, while I love most other.

 

[haruspex]

the reflected polarized intensity is 1.5 times that of the non-polarized reflected intensity.

Where does that come from?
What equations do you have for how reflected intensity depends on polarisation and angle?

 

[Sheepwall]

Nonpolarized wave through polaroid always halves its intensity; When the max value of intensity is reached, the full intensity of the polarized component of the partially polarized wave is let through. Now, the whole intensity of this max is the sum of the halved non-polarized wave and the full polarized wave's intensities, (1/2)*I1+I2 (I1 being the non-polarized wave and I2 being the polarized component). When the minimum value of intensity is reached, none of the polarized component of the wave is let through, so the whole intensity is that of the non-polarized component, divided by 2. The ratio between these values is said to be 4, meaning that:

[(1/2)*I1 + I2]/[(1/2)*I1] = 4

Solving for I2:

I2 = 2*I1 - (1/2)*I1 = (3/2)*I1

I apologize for the terse messages, I've been up all night trying to catch up with schedule, reading a text with barely any explanations or reasonings behind statements about these waves. It has not been a good idea so far.

 

[haruspex]

Nonpolarized wave through polaroid always halves its intensity; When the max value of intensity is reached, the full intensity of the polarized component of the partially polarized wave is let through. Now, the whole intensity of this max is the sum of the halved non-polarized wave and the full polarized wave's intensities, (1/2)*I1+I2 (I1 being the non-polarized wave and I2 being the polarized component). When the minimum value of intensity is reached, none of the polarized component of the wave is let through, so the whole intensity is that of the non-polarized component, divided by 2. The ratio between these values is said to be 4, meaning that:

[(1/2)*I1 + I2]/[(1/2)*I1] = 4

Solving for I2:

I2 = 2*I1 - (1/2)*I1 = (3/2)*I1

I apologize for the terse messages, I've been up all night trying to catch up with schedule, reading a text with barely any explanations or reasonings behind statements about these waves. It has not been a good idea so far.

I'm no expert on this subject, but I thought you could consider the original beam as composed of s-polarised and p-polarised (equal intensities). The min through the polaroid would be the p component and the max would be the s component. There are equations for what fraction of each is reflected given the incident angle and the refractive index.

 

[ehild]

Browse "Fresnel reflection coefficients".