Chapter 23, Problem 16Q

To determine

To Explain:

That it is possible for a light ray travelling in air be totally reflected when it strikes a smooth water surface if the incident angle is chosen correctly.

Answer to Problem 16Q

Solution:

It is not possible for a light ray travelling in air be totally reflected when it strikes a smooth water surface even if the incident angle is chosen correctly. Because, total internal reflection can occur only when light is travelling from higher refractive index medium to a lower refractive index medium.

As the light is travelling in air and strikes on water, it is going from the lower refractive index medium into the higher, the light cannot be totally reflected in the air medium.

Explanation of Solution

When light passes from one material into a second material, where the index of refraction is less (say, from water into air), the refracted light ray bends away from the normal, as for rays J. At a particular incident angle, the angle of refraction will be 90°, and the refracted ray would skim the surface (ray K). The incident angle at which this occurs is called the critical angle,

The Snell’s law, is given by

$\frac{\sin {\theta }_c}{\sin 90}=\frac{n_2}{n_1}$

$\sin {\theta }_c=\frac{n_2}{n_1}\sin 90=\frac{n_2}{n_1}$

This is depicted by the figure.

For any incident angle less than ${\theta }_c$, there will be a refracted ray. However, for incident angles greater than ${\theta }_c$, Snell’s law would tell us that ${\theta }_2(=\frac{n_2}{n_1}\sin 90)$ would be greater than 1.00 when $n_1>n_2$.Yet the sine of an angle can never be greater than 1.00. In this case there is no refracted ray at all, and all of the light is reflected, as for ray L. This effect is called total internal reflection.