Resorting to the Fresnel equations, demonstrate that light reflected from the surface of dielectric will be totally polarized if the angle of incidence `theta_(1)` satisfies the condition `tan theta_(1) = n`, where `n` is the refractive index of the dielectric. What is in this case the angle between the reflected and refracted rays?

Explanation

Fresnel equations read
`I'_(_|_) = I_(_|_) (sin^(2)(theta_(1) - theta_(2)))/(sin^(2)(theta_(1) + theta_(2)))` and `I'_(||) = I_(||) (tan^(2)(theta_(1) - theta_(2)))/(tan^(2)(theta_(1) + theta_(2)))`
At the boundary between vacuum and a dielectric `theta_(1) = theta_(2)` since by Snel's law
`sin theta_(1) = n sintheta_(2)`
Thus `I'_(_|_)//I_(_|_)` cannot be zero. However, if `theta_(1) + theta_(2) = 90^(@), I'_(||) = 0` and the reflected light is polarized in this case. The condition for this is
`sin theta_(1) = n sin theta(2), = n sin(90^(@) - theta_(1))`
or `tan theta_(1) = n theta_(1)` is called Brewsta's angle.
The angle between reflected light and refracted light is `90^(@)` in this case.