Question

Three polaroid sheets $P_1, P_2$ and $P_3$ are kept parallel to each other such that the angle between pass axes of $P_1$ and $P_2$ is $45^\circ$ and that between $P_2$ and $P_3$ is $45^\circ$. If unpolarised beam of light of intensity $128 Wm^{-2}$ is incident on $P_1$. What is the intensity of light coming out of $P_3$?

• A. $128 \,Wm^{-2}$
• B. 0
• C. $16 \,Wm^{-2}$
• D. $64\, Wm^{-2}$

Answer 1

Answer: (C)

$16 \,Wm^{-2}$

Answer 2

We have unpolarised beam's intensity
$I _{0}=128 w / m ^{2}$
Using Malu's law we have
$I=I_{0} \cos ^{2} \theta$
When beam passed from the first polaroid,
$I=I_{0} / 2$
Again, as the angle between $p _{1}$ and $p _{2}$ is $45^{\circ}$,
beam intensity when it will pass $p _{2}$ would be
$l _{1}= I _{0} / 2 \cos ^{2} 45^{0}= I _{0} / 4$
And, also the angle between $p _{2}$ and $p _{3}$ is $45^{\circ}$,
beam intensity when it will come out of $p _{3}$ will be
$l _{2}=I_{0} / 4 \cos ^{2} 45^{0}=I_{0} / 8$
$=128 / 8=16 w / m ^{2}$