Unpolarised light is passed through a polaroid `P_(1)`. When this poalrised beam passes through another polaroid `P_(2)`, and if the pass axis of `P_(2)` makes an angle `theta` with pass axis of `P_(1)`, then write the expression for the polarised beam passing through `P_(2)`. Draw a plot showing the variation of intensity when `theta` varies from 0 to 2 `pi`.

Explanation

It is based on Law of Malus According to this law, when a completely polarised light is
incinent on an analyser , then the intensity of transmitted light varies directly as the
square of cosine of an angle between plane of polariser and plane of analyser.
`therefore I = I _(0) cos^(2) theta`
If the amplitude of transmitted light is a .
then, ` a = a_(0) cos^(theta) therefore a^(2) = a_(0) cos^(2) theta`
`therefore I = I _(0) cos^(2) theta rArr I alpha cos^(2) theta`
`therefore ` Veries from 0 to ` 2 pi and [ cos ^(2) theta] _(av) = (1)/(2pi) underset(0)overset(2) intcos ^(2) theta d theta`
`= (1)/(2pi) underset(0)overset(2pi) int(1 + cos ^(2) theta)/(2) d theta = (1)/(2pixx2) [0 + (sin2 theta)/(2)]^( 2pi) = (1)/(2) = I = I _(0) xx(1)/(2)`