A third polaroid is placed between P1 and P2 with its pass axis making an angle - with the pass axis of P1- Find a value of - for which the intensity of light emerging from P2 is l0-8 where l0 is the intensity of light on the polaroid P1-

Intensity of light coming out polariser P_1=I_02 Intensity of light coming out polariser P_3=I_02cos^2β Intensity of light coming out polariser P ...

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Standard X

Physics

Snell's Law

A third polar...

Question

A third polaroid is placed between $P_{1}$ and $P_{2}$ with its pass axis making an angle $θ$ with the pass axis of $P_{1}$ . Find a value of $θ$ for which the intensity of light emerging from $P_{2}$ is $l_{0} / 8$ where $l_{0}$ is the intensity of light on the polaroid $P_{1}$ .

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Solution

Intensity of light coming out polariser $P_{1} = \frac{I_{0}}{2}$
Intensity of light coming out polariser $P_{3} = \frac{I_{0}}{2} {cos}^{2} β$
Intensity of light coming out polariser $P_{2} = \frac{I_{0}}{2} {cos}^{2} β {cos}^{2} (90 - β)$
$= \frac{I_{0}}{2} {cos}^{2} β {sin}^{2} β$
$= \frac{I_{0}}{2} [\frac{(2 cos β . sin β)^{2}}{2}]$
$I = \frac{I_{0}}{8} (sin 2 β)^{2}$
But it is given that intensity transmitted from $P_{2}$ is
$I = \frac{I_{0}}{8}$
So, $\frac{I_{0}}{8} = \frac{I_{0}}{8} (sin 2 β)^{2}$
or, $(sin β)^{2} = 1$
$sin 2 β = sin \frac{π}{2} \Rightarrow β = \frac{π}{4}$

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A third polaroid is placed between P1 and P2 with its pass axis making an angle θ with the pass axis of P1. Find a value of θ for which the intensity of light emerging from P2 is l0/8 where l0 is the intensity of light on the polaroid P1.

A third polaroid is placed between $P_{1}$ and $P_{2}$ with its pass axis making an angle $θ$ with the pass axis of $P_{1}$ . Find a value of $θ$ for which the intensity of light emerging from $P_{2}$ is $l_{0} / 8$ where $l_{0}$ is the intensity of light on the polaroid $P_{1}$ .