When red light in vacuum is incident at the Brewster angle on a certain glass slab, the angle of refraction is$\mathbf{32}\mathbf{°}$ .What are (a) the index of refraction of the glass and (b) the Brewster angle?

Angle of refraction,${\theta }_r=32°$

We use the formula for Brewster angle to find the refractive index of glass. The addition of Brewster angle and the angle of refraction is$\mathbf{90}\mathbf{°}$.Using this concept, we can find the angle of refraction.

Formulae:

${\theta }_B=ta{n}^{-1}\left(\frac{n_2}{n_1}\right)$

${\theta }_B+{\theta }_r=90°$

The addition of Brewster angle and the angle of refraction is $90°$, i.e.${\theta }_B+{\theta }_r=90°$,

We have${\theta }_r=32°$.

Therefore,

$$\begin{gathered} {\theta }_B+32°=90° \\ {\theta }_B=58°······\left(1\right) \end{gathered}$$

TheBrewster angle given by equation $33-49$is

${\theta }_B=ta{n}^{-1}\left(\frac{n_2}{n_1}\right)$

If the incident and reflected rays travel in air, we can approximate$n_1$as unity and let$n$be the refractive index of the second medium. Then we have

$$\begin{gathered} {\theta }_B=ta{n}^{-1}n \\ {n}_{glass}=tan{\theta }_B \\ =tan58° \\ =1.60 \end{gathered}$$

Hence, the index of refraction of glass is 1.60.

As calculated in part a), from equation (1), we can say that the Brewster angle is$58°$.

Hence, Brewster angle is$58°$.