Question

A thin rectangular polarizer P1 with x-axis as pass axis is kept at the origin. Another identical

polarizer P2 with z-axis as the pass axis is kept parallel to P1 at y=d. A Half Wave Plate (HWP) is

introduced between P1 and P2 with its optic axis making 450 with the pass axis of P1. An

unpolarized light propagating along y-axis is incident normally on P1 from the left hand side.

What would be the state of polarization after P1, half wave plate and P2?​

Answer 1

Answer:

Explanation:

Intensity of light coming out polariser P  

1

​  

=  

2

I  

0

​  

 

​  

 

Intensity of light coming out polariser P  

3

​  

=  

2

I  

0

​  

 

​  

cos  

2

β

Intensity of light coming out polariser P  

2

​  

=  

2

I  

0

​  

 

​  

cos  

2

βcos  

2

(90−β)

=  

2

I  

0

​  

 

​  

cos  

2

βsin  

2

β

=  

2

I  

0

​  

 

​  

[  

2

(2cosβ.sinβ)  

2

 

​  

]

I=  

8

I  

0

​  

 

​  

(sin2β)  

2

 

But it is given that intensity transmitted from P  

2

​  

 is

I=  

8

I  

0

​  

 

​  

 

So,    

8

I  

0

​  

 

​  

=  

8

I  

0

​  

 

​  

(sin2β)  

2

 

or,  (sinβ)  

2

=1

sin2β=sin  

2

π

​  

⇒β=  

4

π

​