How Do You Calculate θ for Polarized Light Intensity Reduction to I0/4?

[jraek1987]

Homework Statement

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.

Homework Equations

I = (1/2)Io

I = Io*cos^2θ

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..

 

[collinsmark]

Hello jraek1987,

Welcome to Physics Forums!

Homework Statement

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.

Homework Equations

I = (1/2)Io

I = Io*cos^2θ

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..

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. )