Question

In Fig. 33-35, light travels from material a, through three layers of other materials with surfaces parallel to one another, and then back into another layer of material a. The refractions (but not the associated reflections) at the surfaces are shown. Rank the materials according to index of refraction, greatest first. (Hint: The parallel arrangement of the surfaces allows comparison.

Short answer

The ranking of materials according to the index of refraction is $n_d>n_b>n_c>n_a$.

Step-by-step solution

The given data

The given figure of light transmission gives the change of light path through three different layers b, c, and d due to refraction.

Understanding the concept of bending due to refraction

For a material with a higher refractive index, the light bends towards the normal line; while for a material with a low refractive index, it speeds up and bends away from the normal line.

Calculation of ranking of materials according to refractive index

When light travels from a rarer to a denser medium, it refracts towards the normal, and when it travels from a denser to a rarer medium, it refracts away from the normal.

Analyzing the given figure according to this, we can write that

$$\begin{gathered} n_b>n_a \\ {n}_b>n_c \\ {n}_d>n_c \\ {n}_d>n_a \end{gathered}$$

From this, we can conclude that

$n_d>n_b>n_c>n_a\mathrm{or}{n}_d>n_b>n_a>n_c$

The angle made by the light ray with the surface in material a is greater than that with material c.

Hence, by Snell’s law, $n_c>n_a$

Therefore, the ranking of the materials is$n_d>n_b>n_c>n_a$