Chapter 18, Problem 88A

To determine

The pair of media which has the smaller critical angle.

Answer to Problem 88A

Air and float glass

Explanation of Solution

Introduction:

When a ray of light moves from a medium of higher index of refraction in to a medium with a lower index of refraction, then light reflects back to its incident medium for certain angles. This phenomenon is known as total internal reflection. And, the angle of incidence at which the ray of line lines along the boundary of the mediums is called critical angle which is given as,

  $\sin {\theta }_c=\frac{n_2}{n_1}$

Here, $n_1$ is the index of refraction of incident medium and $n_2$ is the index of refraction of refracting medium.

Now it can be written that,

  $\frac{n_{air}}{n_{water}}>\frac{n_{air}}{n_{glass}}$

And, since the critical angle is directly proportional to the above ratio of index of refraction of mediums. Therefore, the air-float glass pair will have smaller critical angle.

Conclusion:

The air-float glass pair will have smaller critical angle as that of the air-water pair.