Two polaroids P_{1} and P_{2} are placed with their pass axes perpendicular to each other. An unpolarised light of intensity *I*_{o} is incident on P_{1}. A third polaroid P_{3} is kept in between P_{1} and P_{2} such that its pass axis makes an angle of 45° with that of P_{1}. Determine the intensity of light transmitted through P_{1}, P_{2} and P_{3}

#### Solution

As given in the question, the polaroids P_{1} and P_{2} are placed with their pass axes perpendicular to each other. Also, P_{3} is placed at an angle of 45° with respect to P_{1}.

Now, we have:

Intensity of light after falling on P_{1 }`I'=I_0/2`

Intensity of light after falling on P_{3} I"=

`I'cos^2(theta)=I_0/2cos^2(45^@)=I_0/4`

Therefore, a light of intensity `I_0/4`will pass through P_{3} and the angle between P_{3} and P_{2} will be 45° because of the condition given in the question.

Intensity of light after falling on P_{2 }I''' = I'' `cos^2(theta)=I_0/4cos^2(45^@)=I_0/8`