Two polaroids are kept corssed `("transmission axes at " 90^(@))` to each other.
(i) What will be the intensity of the light coming out from the seond polaroid when an unpolarised light of intensity I falls on the first polaroid?
(ii) What will be the intensity of light coming out from the second polaroid if a thrid polaroid is kept at `45^(@)` inclination to both of them.

Explanation

(i) As the intensity of th umpolarised light falling on the first polaroid is I, the intensity of polarized light emerging from it will be `I_(0)=((1)/(2)).` Let I. be the intensity of light emerging from the second polaroid.
Malus. law, `I. = I_(0) cos^(2) theta`
Here `theta is 90^(@)` as the transmission axes are perpendicular to each other.
Substituting. `1.=((1)/(2))cos^(2)(90^(@))=0" " [thereforecos(90^(@))=0]`
No light comes out from the second polaroid.
(ii) Let the first polaroid be ` P_(1)` and the second polaroid `P_(2)`. They are oriental at `90^(@)`. The third polaroid `P_(1)` introduced between them `45^(@)`. Let I. be the intensity of light emerging from `P-(3)`.
Angle between `P_(1) and P_(3) is 45^(@)`. The intensity of light coming out from `P_(3) is I. = I_(0) cos^(2) theta`
Substituting, `I.=((1)/(2))cos^(2)(45^(@))=((1)/(2))((1)/(sqrt(2)))^(2)=(1)/(4):I.(1)/(4)`
Angle betweem `P_(3) and P_(2) is 45^(@)` . Let I. is the intensity of light coming ut coming `P_(2) I. = I.cos^(2) theta`.

Here, the intensity of polarized light existing between `P_(3)` and `P_(2) " is" (1)/(4)`.
Substituting, `1^(n)=((1)/(4))cos^(2)(45^(@))=((1)/(4))((1)/(sqrt(2)))^(2)=(1)/(8)`
`1^(n) = (1)/(8)`