Ask Me Help Desk - How do we work out answers to questions that have 3 polarisers for physics?

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".