Chapter 18, Problem 98A

To determine

The value of $n=\frac{\sin {\theta }_1}{\sin {\theta }_2}$ from the general form of Snell’s law of refraction.

Answer to Problem 98A

The value of $n=\frac{\sin {\theta }_1}{\sin {\theta }_2}$ from the general form of Snell’s law of refraction is derived.

Explanation of Solution

Given info:

The Snell’s law of refraction is $n_1\sin {\theta }_1=n_2\sin {\theta }_2$ .

Calculation:

Assume that the light rays are parallel and straight beam of light and the medium in which the light enters is an isotropic medium.

Consider the substance 1 be air.

The angle of incidence must be in air.

Hence, the index of refraction of medium 1, $n_1=1.000$ .

Consider the index of refraction ofmedium 2, $n_2=n$ .

Apply Snell’s law of refraction as follows:

  $\begin{array}{l}{n}_1\sin {\theta }_1=n_2\sin {\theta }_2\\ \left(1.000\right)\sin {\theta }_1=n\sin {\theta }_2\\ n=\frac{\sin {\theta }_1}{\sin {\theta }_2}\end{array}$

Hence, the value of $n=\frac{\sin {\theta }_1}{\sin {\theta }_2}$ from the general form of Snell’s law of refraction is derived.

Restriction:The Snell’s law is not applicable when the light ray isincident normal to the surface of the medium as both the angle of incidence and angle of refraction is zero.