Question

What is Brewster’s angle for light traveling in water that is reflected from crown glass?

Short answer

The Brewster's angle is \({48.8^\circ }\).

Step-by-step solution

Definition of Brewster’s angle

Brewster's angle is the angle of incidence at which light of a specific polarisation passes through a clear dielectric surface perfectly without reflection.

Finding Brewster’s angle

The equation is used to solve this problem\(\tan \left( {{\theta _b}} \right) = \dfrac{{{n_2}}}{{{n_1}}}\) where \({n_1}\) is the index of reflection for water and for water, is the index of reflection, while for crown glass, is the index of redfraction \({n_2}\)

\(\begin{aligned}\tan \left( {{\theta _b}} \right) &= \dfrac{{{n_2}}}{{{n_1}}}\\ &= \dfrac{{1.52}}{{1.33}}\\ &= 1.14\end{aligned}\)

Solving for the angle, we get

\(\begin{aligned}{c}{\theta _b} &= {\tan ^{ - 1}}(1.14)\\ &= {48.8^\circ }\end{aligned}\)

Therefore, the Brewster's angle is \({\rm{48}}{\rm{.}}{{\rm{8}}^{\rm{^\circ }}}{\rm{.}}\)