Intensity of polaroids at an angle

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SUMMARY

The discussion focuses on determining the angle at which two Polaroids should be oriented to reduce the intensity of unpolarized light by specified factors after the first Polaroid. The first Polaroid halves the intensity, resulting in I1 = 0.5I0. The second Polaroid's intensity is calculated using the equation I2 = I1(cos θ)², where θ is the angle between the axes of the Polaroids. The user initially misinterprets the reduction factors, leading to incorrect calculations for θ, specifically arriving at 32 degrees for a factor of 7, which is incorrect.

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Homework Statement


At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in half) of 7? b) 25? c) 250?

Homework Equations



The first polaroid decreases the intensity by 1/2, so that's I1 = 0.5I0.
I also have I2 = I1(cos theta)^2.

The Attempt at a Solution



I think it might just be the wording that's getting me, but here's my interpretation:

In the first polaroid, 1/2 the intensity is removed. That makes I1 equal to 0.5 I0.
In the second polaroid, 1/7 of I0 is removed. That makes I2 = 0.5I0 - (1/7 I0), or 5/14 I0.

So then I've got I2 = I1(cos theta)^2 --> 5/14 I0 = 0.5 I0 cos(theta)^2. This gives me 32 as theta, which is incorrect. I haven't tried to work out the rest as there seems to be something wrong with my procedure and they're all essentially the same problem.

Any help is much appreciated!
 
Physics news on Phys.org
To reduce I1 by a factor of 7 means that

I2 = (1/7) I1
 

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