Chapter 18, Problem 53A

To determine

The angle of refraction in air.

Answer to Problem 53A

There will be no refraction and light will undergo total internal reflection.

Explanation of Solution

Given:

The angle of incidence in water, ${\theta }_1=55.0°$ .

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, $n{2}_{}=1.0003$

Index of refraction of water, $n{1}_{}=1.33$

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

  $\begin{array}{c}{n}_1\sin {\theta }_1=n_2\sin {\theta }_2\\ \left(1.33\right)\sin 55°=\left(1.0003\right)\sin {\theta }_2\\ \sin {\theta }_2=1.089\text{, which is not possible}\end{array}$

Conclusion:

Above thing is not possible, thus no refraction will occur and the light will undergo total internal reflection.