If a ray of light is incident on a reflecting medium at the polarising angle, prove that the reflected and the refracted rays are at `90^(@)` to each other.

Explanation

Let a ray of light AO be incident on XY at the polarising angle P. The reflected ray OB, which is plane polarised, also makes an angle P with the normal.
Let the angle of reflection be r.
According to Brewster's law, tan ""p = `mu` [ where `mu` = refractive index of the medium]
According to the law of refraction,
`mu = (sinangleAON)/(sinangleN'OC) = (sin p)/(sinr)`
`therefore " "tanp = (sinp)/(sinr) " " or, (sinp)/(cosp) = (sinp)/(sinr)`
or, `sin r = cosp = sin(90^(@)-p) or, r = 90^(@) - p`
`therefore` `r+ p = 90^(@)`
So, the reflected ray OB and the refracted ray OC are at `90^(@)` to each other .