# Calculate theta from an unpolarized beam of light and two ideal polarizing sheets

1. Apr 25, 2012

### jraek1987

1. The problem statement, all variables and given/known data
An unpolarized beam of light has intensity Io. It is incident on two ideal polarizing sheets. The angle between the axes of polarization of these sheets is θ. Find θ if the emerging light has intensity Io/4.

2. Relevant equations
I = (1/2)Io

I = Io*cos^2θ

3. The attempt at a solution
If I = Io/4 then the second equation becomes:

Io/4 = Io*cos^2θ

Solving for θ gives:

(Io/4) = Io*cos^2θ
*1/Io {both sides}

1/4 = cos^2θ

√(1/4) = √(cos^2(θ))

1/2 = cosθ
*1/cos {both sides}

cos^-1(1/2) = θ

**The book gives the answer of cos^-1(1/√2) = θ

Not sure what I did wrong..

2. Apr 25, 2012

### collinsmark

Hello jraek1987,

Welcome to Physics Forums!

I0/4 is the intensity after the light passes through the second polarizer. I0 is the inensity of the light before it passes through the first polarizer.

You've neglected to take into account the intensity change caused by the first polarizer. (i.e. what is the intensity of the light in between the polarizers?)

(Hint: remember, the initial light I0 is unpolarized. )