Polarisers and Malus's Law

RosSin · Apr 9, 2009, 11:14 PM

Q. Unpolarized light of intensity Io is incident on a stack of 2 polarizers, and intensity I emerges from the last polarizer. If the angle between the polarizers is 45 degrees, what is the ratio I/Io?

A 0.707
B 0.500
C 0.866
D 0.250
E 0.354

Thanks in advance

Perito · Apr 10, 2009, 05:26 AM

Malus' law is

$I=I_o\,cos^2(\theta)$

where $\theta$ is the angle of rotation of the plane of polarization. One can rearrange the equation by dividing both sides by zero to get

$\frac{I}{I_o}=cos^2(\theta)$

If the angle, $\theta$ is 45 degrees, the problem becomes trivial:

$\frac{I}{I_o}=cos^2(45^o)$ and

$cos(45)=\frac{\sqrt2}{2}$ so

$\frac{I}{I_o}=\frac 12$

So, your answer is B

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