Question

You are provided with three polarizers with filters making angles of (A) 90 ​∘ ​​ , (B) 180 ​∘ ​​ and (C) −45 ​∘ ​​ with respect to the vertical. You want to maximize the transmission through the set of three polarizers. What order provides you with maximum transmission?

Answer 1

Order of maximum transmission of the polarizer is A, C and B.

Solution:

As per the question:

For the first polarizer, the angle is quite insignificant:

(A)
`90^(\circ)`:

The light intensity after passing through the first polarizer is
`I_(o)` and this intensity does not depend on the angle of the polarizer.

Consider
`90^(\circ)` with the vertical, the intensity is given by:

`I = I_(o)cos^(2)90^(\circ)`

`I = I_(o)cos(2(45^(\circ))) = I_(o)((1+cos90^(\circ)))/(2) = (I_(o))/(2)`

(B)
`180^(\circ)`:

Suppose the second polarizer is
`45^(\circ)` with the vertical.

Now, intensity through the second polarizer:

`I' = Icos^(2)(\theta_(2) - \theta_(1)) = (I_(o))/(2)cos^(2)(- 45 - 90)`

`I' =  (I_(o))/(2)cos^(2)135^(\circ) = (I_(o))/(4)`

Now, if we consider the second polarizer to be
`180^(\circ)`,

`I' = (I_(o))/(2)cos^(2)180^(\circ) = (I_(o))/(2)cos^(2)(180^(\circ) - 90^(\circ)) = 0`

(C)
`- 45^(\circ)`:

Now,

Intensity through the third polarizer, if it is
`180^(\circ)` with the vertical:

`I' = Icos^(2)(\theta_(2) - \theta_(1)) = (I_(o))/(2)cos^(2)(180 - (- 45))`

`I' = (I_(o))/(8)`