Question

In a stack of three polarizing sheets the first and third are crossed while the middle one has its axis at 45°
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
(1) 1/2
(2) 1/3
(3) 1/4
(4) 1/8
​

Answer 1

Given :

Three polarizing sheets are there .

Angle between 1st and 3rd polarizer :

= 90°

Angle between 1st and 2nd polarizer :

= 45°

To Find :

Fraction of intensity of an incident unpolarized light transmitted by the stack =?

Solution :

We know that when an unpolarized light passes through a polarizer its intensity gets halved .

Now according to Malus ' Law :

If the axis of two polarizers ar at angle of $\theta$ then fraction of intensity thta passes out through 2nd polarizer is :

$I=I_{0}$

So the intensity of after passing through 1st polarizer will be :

$I_{1}=\frac{I_{0}}{2}$

After passing through :

$I_{2}= \frac{I_{0}}{2} \times cos^{2} 45\degree\\\\I_{2}=\frac{I_{0}}{4}$

After passing through 3rd polarizer :

$I_{3}= \frac{I_{0}}{4} \times cos^{2} 45\\\\I_{3}=\frac{I_{0}}{8}$

So finally the  fraction of intensity of beam after coming the stack of three polarizers will be 1/8.