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

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".