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:

Answer 1

Answer:

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 \thetaθ then fraction of intensity thta passes out through 2nd polarizer is :

I=I_{0}I=I

0

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

\begin{lgathered}I_{1}=\frac{I_{0}}{2} \\\end{lgathered}

I

1

=

2

I

0

After passing through :

\begin{lgathered}I_{2}= \frac{I_{0}}{2} \times cos^{2} 45\degree\\\\I_{2}=\frac{I_{0}}{4}\end{lgathered}

I

2

=

2

I

0

×cos

2

45°

I

2

=

4

I

0

After passing through 3rd polarizer :

\begin{lgathered}I_{3}= \frac{I_{0}}{4} \times cos^{2} 45\\\\I_{3}=\frac{I_{0}}{8}\end{lgathered}

I

3

=

4

I

0

×cos

2

45

I

3

=

8

I

0

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