Chapter 24, Problem 55P

To determine

The Brewster’s angle for a diamond.

Answer to Problem 55P

  $61.2°$ .

Explanation of Solution

Given:

Refractive index of diamond, $n_{diamond}=2.42$

Refractive index of water, $n_{water}=1.33$

Formula used:

It is known that: $\tan {\text{θ}}_{\text{p}}=\frac{{\text{n}}_{\text{diamond}}}{n_{water}}$

Where,

  ${\text{θ}}_{\text{p}}$ is Brewster’s angle.

  $n_{diamond}$ is refractive index of diamond.

  $n_{water}$ is refractive index of water.

Calculation:

Substitute the given data into the formula ${\text{tanθ}}_{\text{p}}\text{=}\frac{{\text{n}}_{\text{diamond}}}{{\text{n}}_{\text{water}}}$ to get the Brewster’s angle for a diamond.

  $\tan {\text{θ}}_{\text{p}}=\frac{2.42}{1.33}$

  $\therefore {\text{θ}}_{\text{p}}={\tan }^{-1}\left(1.82\right)$

  $\therefore {\text{θ}}_{\text{p}}=61.2°$

Conclusion:

The required Brewster’s angle is $61.2°$ .