Question

Could you please demonstrate Brewster's angle and Critical angle in equation form and how to solve for it. still don't understand. Thank you

Answer 1

Brewster's angle ( i_p ) is the incidence angle at which the angle between the reflected and refracted rays is 90^o

An in this situation the reflected light will be linearly polarized.
Now what will be angle of refraction? So you will get angle of refraction r = 90 - i_p

Now according to the Snell's Law

( where n₂ is the refractive index of second the medium and n₁ is the refractive index of the first medium )

or

or

[ as sin (90 -i_p) = cosi_p ]

or

---------------------------- (1)

Critical angle (i_c) is the incidence angle at which the angle refraction r become 90^o
Here it is necessary that ray of light should pass from optically denser medium to rarer medium.

Now according to the Snell's Law

( where n₂ is the refractive index of second the medium and n₁ is the refractive index of the first medium and n₁>n₂ )

or

or

[ as sin (90) = 1] ----------------------------- (2)

if second medium is air then n₂ = 1 and refractive index of first medium is n

Then

From equation (1) and (2) for a given pair of medium