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## Homework Statement

A beam of polarized light is sent through a system of two polarizing sheets. Relative to the polarization direction of that incident light, the polarizing directions of the sheets are at angles θ for the first sheet and 90° for the second sheet. If 0.10 of the incident intensity is transmitted by the two sheets, what is θ?

## Homework Equations

I1 = Io /2

I2 = I1 * cos^2(θ)

## The Attempt at a Solution

The intensity of the beam after the first polarizing sheet is as follows:

I1 = Io /2

The intensity of the beam after the second polarizing sheet is as follows:

I2 = I1 * cos^2(θ)

Where θ is the angle difference between θ1 and θ2.

The problem tells you that the transmitted beam is 0.10 of the original beam:

I2 = 0.10 * Io

Substituting with the equations above:

I2 = 0.10 * Io = (Io/2) * cos^2(θ) and therefore:

0.10 = cos^2(θ)/2

Solving for θ:

θ =arccos([itex]\sqrt{0.2}[/itex])= 63°

Which means the angle of the first polarizing sheet is 63° out from 90° so the answer I get is:

27° or 153°

But this isn't correct according to the back of the book. Please help. Thanks in advance, MrMoose