Question

Two polarizing plates have polarizing directions parallel so as to transmit maximum intensity of light. Through what angle must either plates be turned if the intensity of the transmitted beam is one third the intensity of incident beam.

Answer 1

Solution:

We know that when two polarising plates have polarising direction in parallel than intensity is,

$I=I_0 \cos2θ$

When intensity of beam is transmitted then its intensity drop to 1/3.

 Therefore,

$I=\dfrac 13I_0$

Now,

$\dfrac 13I_0=I_0 \cos2θ \\ \Rightarrow \dfrac 13= \cos2θ \\ \Rightarrow 2θ=\cos^{-1}\dfrac 13 \\ \Rightarrow θ=35.26438^{\circ \:},\:θ=144.73561^{\circ \:}$