Question

In a stack of three polarizing sheets the first and third are crossed while the middle one has its axis at ${45}^{\circ }$ to the axes of the other two. The fraction of the intensity of an incident unpolarized beam of light that is transmitted by the stack is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{8}$

Answer 1

The correct option is D $\frac{1}{8}$

We know that when an unpolarized light passes through a polarizer its intensity gets halved.
Now according to Malu's law-
$I=I_0$
So the intensity after passing through $1^{st}$ polarizer will be
$I_1=I_0{\cos }^2\theta =I_0{\cos }^2{45}^{\circ }=\frac{I_0}{2}$
After passing through $2^{nd}$ polarizer
$I_2=I_1{\cos }^2\theta =\frac{I_0}{2}\times \frac{1}{2}=\frac{I_0}{4}$
After passing through $3^{rd}$ polarizer
$I_3=I_2{\cos }^2\theta =\frac{I_0}{4}\times \frac{1}{2}$
$I_3=\frac{I_0}{8}$