# Polarizing Filters Question

1. Nov 16, 2014

### Chase11

1. The problem statement, all variables and given/known data
Unpolarized light passes through 4 polarizing filters. The polarizing direction of each filter is offset by 25 degrees from the filter in front of it. Find the fraction of light that gets through all four filters.

2. Relevant equations
I=I0Cos2θ

3. The attempt at a solution
From my class notes, the professor worked a very similar problem in which there were two polarizing filters. He used (1/2)I0Cos2θ to solve for the answer. So I used (1/4)I0Cos2θ and got .2053, and the answer is supposed to be .277. Can someone please explain what I am doing wrong here?

2. Nov 16, 2014

### Orodruin

Staff Emeritus
Think of this problem step by step rather than just finding an equation to plug things into: How much intensity remains after the first filter? How much after the second? How (in what polarisation) does the light arrive at the second filter? How does it arrive at the third? What is then the intensity after the third? Etc.

3. Nov 16, 2014

### Chase11

Okay so I tried solving that equation each time for every filter. I started with simply cos(25)^2, Then used the answer as I0 for the next filter (So .82139*Cos(25)^2) etc.. I am still getting the wrong answer. Does the angle itself change between each filter? My interpretation is that the angle is 25 degrees between each filter.

4. Nov 16, 2014

### Orodruin

Staff Emeritus
Try thinking about what is actually happening at the first filter - remembering that the light arriving at the first filter is unpolarised.

5. Nov 16, 2014

### Chase11

The orientation of the light is changed by 25 degrees, correct?

6. Nov 16, 2014

### Orodruin

Staff Emeritus
What is the orientation of unpolarised light?

7. Nov 16, 2014

### Chase11

Isn't it all random?

8. Nov 16, 2014

### Orodruin

Staff Emeritus
Exactly, but the light exiting the first filter is not. So if you have unpolarised light before the first filter, what is the intensity after? (We have already settled that it will be polarised after, then you can think of what happens to the polarised light when it passes the remaining filters.)

9. Nov 16, 2014

### Chase11

Oh okay I got it, so I was using the wrong equation for the first step. Thanks!