Chapter 18.1, Problem 3PP

To determine

The angle of refraction when light travels from air into diamond.

Answer to Problem 3PP

  $16.97°$

Explanation of Solution

Given:

The angle of incidence of the light, ${\theta }_1=45°$

Formula used:

Snell’s law of refraction,

  $n_1\sin {\theta }_1=n_2\sin {\theta }_2$

Where,

  $\begin{array}{l}{n}_1=\text{ index of refraction of first medium}\\ n_2=\text{ index of refraction of second medium}\\ {\theta }_1=\text{ angle of incidence}\\ {\theta }_2=\text{ angle of refraction}\end{array}$

Calculation:

It is known that,

Index of refraction of air, $n{1}_{}=1$

Index of refraction of diamond, $n{2}_{}=2.42$

Then, using Snell’s law of refraction, angle of refraction will be,

  $\begin{array}{c}{n}_1\sin {\theta }_1=n_2\sin {\theta }_2\\ \left(1\right)\sin 45°=\left(2.42\right)\sin {\theta }_2\\ {\theta }_2={\sin }^{-1}\left(0.292\right)\\ =16.97°\end{array}$

Conclusion:

Hence, the angle of refraction is $16.97°$ .