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RosSin · Apr 9, 2009, 11:22 PM

Q. Unpolarized light of intensity Io is incident on a stack of 3 polarizers, and intensity I emerges from the last polarizer. If the angles of the three polarizers are 0 degrees, 30 degrees and 70 degrees with respect to vertical what is the ratio I/Io?

A 0.088
B 0.660
C 0.220
D 0.440
E 0.044

Thanks in advance

Perito · Apr 10, 2009, 05:46 AM

Starting with Malus' law, again

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

or

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

This time you have two experiments because you have three polarizers. The first pair rotates the light by 30 degrees; the second pair rotates the light by 70 degrees (40 degrees additional). We presume that the same material is present between both sets of polarizers.

So,

$\frac{I_1}{I_o}\,=\,cos^2(30)\, =\, 0.75$

$\frac{I}{I_1}\,=\,cos^2(40)\, =\, 0.587$

therefore

$\frac{I}{I_o}\,=\,\frac{I_1\,}{\,I_o}\,\frac{I}{I_ 1} \,=\,(0.75)\, (0.587)\,=\,0.440$

You could also have solved this in one step:

$\frac{I}{I_o}\,=\,cos^2(30)\,cos^2(40)$

Your answer is "D".