Question

A beam of unpolarised light is incident on a glass-air interface. Show, using a suitable ray diagram, that light reflected from the interface is totally polarised, when μ = tan i_B, where μ is the refractive index of glass with respect to air and i_B is the Brewster's angle.

Answer 1

When unpolarised light is incident on the glass-air interface at Brewster angle i_B, then reflected light is totally polarised. This is called Brewster's Law.

When light is incident at Brewster angle, the reflected component OB and the refracted component OC are mutually perpendicular to each other.

From the figure, we have

∠BOY + ∠YOC = 90⁰

( 900 − i_B ) + ( 90⁰ − r ) = 90⁰

where, r is angle of refraction

90⁰ − i_B = r

According to the Snell's law:

`mu=sini/sinr`

i = i_B and r = (90⁰ − i_B)

`mu=sini_B/sin(90^@-i_B)=sini_B/cosi_B`

μ =tan i_B

Hence proved.