Q. A beam of unpolarised light is incident on two polaroids crossed to each other. When one of the polaroid is rotated through an angle, then 25% of the incident unpolarised light is transmitted by the polaroids. Then the angle through which polaroid is rotated, is

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A beam of unpolarised light is incident on two polaroids crossed to each other. When one of the polaroid is rotated through an angle, then 25% of the incident unpolarised light is transmitted by the polaroids. Then the angle through which polaroid is rotated, is

Solution:

Let $I_0$ be intensity of incident light, then the intensity of light emerging from the first polaroid,

$I_{1}=frac{I_{0}}{2}$

Initially, the two polaroids are crossed to each other i.e. $ theta_{i}= 90^{°}$

Let the polaroid be rotated by angle theta, then the angle between polarising directions is $90^{°}-theta$

Now, intensity of light emerging from the second polaroid,

$I_{2}=I_{1},cos^{2}left(90^{°}-thetaright)=frac{I_{0}}{2} cos^{2}left(90^{°}-thetaright)$

Also, $I_{2}=25%$ of $I_{0}=frac{I_{0}}{4}$

$therefore frac{I_{0}}{4}=frac{I_{0}}{2}cos^{2}left(90^{°}-thetaright)$

$Rightarrow cos^{2}left(90^{°}-thetaright)=frac{1}{sqrt{2}}=cos,45^{°}$

or $theta=90^{°}-45^{°}=45^{°}$