How to Determine the Refractive Index of Glass Using Polarized Light?

[fkf]

Homework Statement

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?

Homework 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

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 let's 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]

Pls post the details of your working.

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?

 

[paranormal]

Your approach is on the right track, but there are a few things that need to be addressed. First, let's review the concept of polarization by reflection. When unpolarized light is incident on a surface at an angle, the reflected light will be partially polarized in the plane of incidence. This means that the electric field of the reflected light will be oscillating in a specific direction. The degree of polarization depends on the angle of incidence and the refractive index of the material.

In this problem, we are given the angle of incidence (37.5°) and the ratio of maximum to minimum intensity (4.0). To solve for the refractive index of the glass, we need to use the Fresnel equations. These equations describe the relationship between the incident, reflected, and transmitted electric fields at an interface between two materials.

To apply the Fresnel equations, we first need to determine the angle of reflection. This can be done using Snell's law, which relates the angle of incidence to the angle of refraction. Once we have the angle of reflection, we can use the Fresnel equations to calculate the ratio of maximum to minimum intensity. This can then be compared to the given ratio to solve for the refractive index of the glass.

In summary, your approach is correct, but you need to use Snell's law to determine the angle of reflection and then apply the Fresnel equations to calculate the ratio of maximum to minimum intensity. From there, you can solve for the refractive index of the glass.