The leftmost block in Fig. 33-33 depicts total internal reflection for light inside a material with an index of refraction${\mathit{n}}_{\mathbf{1}}$when air is outside the material. A light ray reaching point A from anywhere within the shaded region at the left (such as the ray shown) fully reflects at that point and ends up in the shaded region at the right. The other blocks show similar situations for two other materials. Rank the indexes of refraction of the three materials, greatest first.

Figure 33-33 depicting three total internal reflection cases is given.

Total internal reflection refers to the total bending of the light within the material. The light incidents and reflected in the same medium. It occurs when the angle of incidence is greater than an angle which is known as the critical angle.

Formula:

The critical angle of total internal reflection,

${\theta }_c={\sin }^{-1}\frac{n_2}{n_1}$ (i)

Where,$n_2$ is the refractive index of the outside layer or material, and$n_1$ is the material where the reflection occurs.

From the given figure, we can infer the relation between their critical angles as:

${\theta }_1>{\theta }_2>{\theta }_3$

In this case, we are given that,

$n_2\left(\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{air}\right)=1$

$n_1\left(\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{material}\right)=n$

Thus, using equation (i), the critical angle can be given as:

Since, ${\theta }_1>{\theta }_2>{\theta }_3$

Then, according to the above relation (a), we can say that the refractive indexes of the materials vary as: $n_3>n_2>n_1$

Hence, the ranking of the materials is $n_3>n_2>n_1$