Chapter 18, Problem 81A

To determine

To explain: The speed of light change as the index of refraction increases.

Answer to Problem 81A

As the index of refraction increases, the speed of light also decreases.

Explanation of Solution

Introduction:

When the rays of light rays moving in a certain medium, enters another medium, the light ray bends either towards or away from the interface of the two mediums. This measure of the bending of light ray when it enters from one medium to the other is called as index of refraction. Greater the value of index of refraction of a material, higher will be bending of light entering the material.

The expression of light’s speed in a medium is,

  $v=\frac{c}{n}$

Here, $c$ is the light’s speed in vacuum and $n$ is the index of refraction.

From the expression, the light’ speed in a given medium vary inversely with the medium’s refraction index of the medium. This states that, as the medium’s refraction index $\left(n\right)$ increases, the light’s speed $\left(v\right)$ will decrease.

Conclusion:

Thus, the light’s speed will decrease with an increase in the medium’s refraction index.