(a) Light, from a sodium lamp, is passed through two polaroid sheets `P_(1)` and `P_(2)` kept one after the other. Keeping `P_(1)` fixed, `P_(2)` is rotated so the its 'pass-axis' can be at different angles, `theta,` with respect to the pass-axis of `P_(1)`
An experimentalist records the following data for the intensity of light coming out `P_(2)` as a function of the angle `theta.`

[`I_(0)=` Intensity of beam falling on `P_(1)`]
One of these observation is not is agreement with expected theoretical variation of `l.` ldentify this observation and write the correct expression.
(b) Define Brewster angle and write the expression for it in terms of the refractive index of the medium.

Explanation

(a) If `l_(0)` is the irradiate of incoming beam, then the irradiance is reduced to `l_(1)=l_(1)=(l_(0))/(2)` after passing through the first polariser.
`therefore l_(2)=l_(1) cos^(2)30^(@) [therefore l=l_(0) cos^(2) theta]`
`=(l_(0))/(2)((sqrt3)/(2))^(2)=l_(0)/(2)xx(3)/(4)=(3l_(0))/(8)`
`l_(3)=l_(2) cos^(2)45^(@)`
`=(3l_(0))/(8)((1)/(sqrt2))^(2)=(3l_(0))/(8)xx(1)/(2)=(3l_(0))/(16)`
`l_(4)=l_(4) cos^(2)60^(@)`
`=(3l_(0))/(64)xx0=0`
Obesrvations `(3) and (4)` are not in agreement with the expected theoretical variations of `l`. `thereore` Conrrect observations are
`l_(3)=(3l_(0))/(16) and l_(4)=(3l_(0))/(64)`
(b) Brewster's angle : The angle of incidence at which, when ordinary light is incident on transparent refracting medium, the reflected light becomes maximum in plane, polarised light is called Brewster's angle or polarising angle. It is denoted by in.
The relation between retroactive index `mu` and in is `mu=tan i_(p)`.