Chapter 18.1, Problem 7SSC

To determine

The index of refraction of the unknown material.

Answer to Problem 7SSC

  $1.46$

Explanation of Solution

Given:

The angle of incidence, ${\theta }_1=30.0°$

The angle of refraction, ${\theta }_2=20.0°$

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, $n{1}_{}=1$

Then, using Snell’s law of refraction, index of refraction of the other medium will be,

  $\begin{array}{c}{n}_1\sin {\theta }_1=n_2\sin {\theta }_2\\ \left(1\right)\sin 30°=n_2\sin 20°\\ n_2=1.46\end{array}$

Conclusion:

Hence, the index of refraction of the unknown material is $1.46$ .