Polarization and intensity with three polarizing sheets

[VitaX]

Homework Statement

[PLAIN]http://img855.imageshack.us/img855/7899/physicsch3333.png

Homework Equations

I = 0.5*I_0
I = I_0*cos^2(θ)

The Attempt at a Solution

I_1 = 0.5*I_0*(cos 50)^2
I_2 = I_1*(cos 70)^2
I_3 = I2*(cos 50)^2

This is my attempt at the problem. This is new to me and I know that I use I = 0.5*I_0 for unpolarized light, but this one had an angle so I wasn't sure how to implement it in. I'm assuming my I_1 is wrong, what's the correct notation for it? And I used the angles relative to the x axis, should I not do that and use the given angles?

 

[Mike Pemulis]

This is new to me and I know that I use I = 0.5*I_0 for unpolarized light, but this one had an angle so I wasn't sure how to implement it in.

Your I₁ is indeed wrong. The light is initially unpolarized, which means it doesn't point in any direction in particular. So the angle of the first sheet doesn't matter. We just have,

I₁ = 0.5 I₀

And I used the angles relative to the x axis, should I not do that and use the given angles?

You do need to fix your angles. The equation you posted is correct, but you didn't implement it correctly. We have,

I = I₀*cos²(θ)

Any angle is defined as the angle between something and something else. What two things is θ between in this case?

 

[VitaX]

Your I₁ is indeed wrong. The light is initially unpolarized, which means it doesn't point in any direction in particular. So the angle of the first sheet doesn't matter. We just have,

I₁ = 0.5 I₀



You do need to fix your angles. The equation you posted is correct, but you didn't implement it correctly. We have,



Any angle is defined as the angle between something and something else. What two things is θ between in this case?

So it will be:
I₁ = 0.5 I₀
I₂ = I₁cos^2(20)
I₃ = I₂cos^2(40)

Then it's just:
I₃ = I₂cos^2(40) = (I₁cos^2(20))cos^2(40) = 0.5 I₀cos^(20)cos^2(40)

And whatever constant I get multiplied by I₀. Then find the ratio of I₃/I₀ and that's my percentage of light intensity? Are my angles right this time around?

 

[Mike Pemulis]

I₂ = I₁cos²(20)
I₃ = I₂cos²(40)

No -- the given angles are not exactly the angles you plug into the formula. You need to figure out what to do with them. One hint -- say the axis of Sheet 2 pointed in the same direction as the axis of Sheet 1. What would happen to the intensity as the light passed through Sheet 2?

 

[VitaX]

No -- the given angles are not exactly the angles you plug into the formula. You need to figure out what to do with them. One hint -- say the axis of Sheet 2 pointed in the same direction as the axis of Sheet 1. What would happen to the intensity as the light passed through Sheet 2?

So you're telling me to use something like this:

Where I take the sum of the angles 40 and 20 and then my angles for I₂ and I₃ will be 60 degrees? I guess I could find the angle between the two, which would be 120 as well, since we are squaring them, the negative will go away anyways.

 

[Mike Pemulis]

Exactly right. I have nothing to add -- nice job.