Question

The refractive index of a material changes by 0.014 as the colour of the light changes from red to violet. A rectangular slab of height 2.00 cm made of this material is placed on a newspaper. When viewed normally in yellow light, the letters appear 1.32 cm below the top surface of the slab. Calculate the dispersive power of the material.

Answer 1

Given:-

Difference in the refractive indices of violet and red lights = 0.014

Let μ_v and μ_r be the refractive indices of violet and red colours.

Thus, we have:-

μ_v − μ_r = 0.014

Now,

Real depth of the newspaper = 2.00 cm

Apparent depth of the newspaper = 1.32 cm

\[\text{Refractive index }= \frac{\text{Real depth}}{\text{Apparent depth}}\] 

Refractive index for yellow light \[\left( \mu_y \right)\] is given by

\[ \mu_y  = \frac{2 . 00}{1 . 32} = 1 . 515\]

Also,

Dispersive power, \[\omega = \frac{\mu_v - \mu_r}{\mu_y - 1}\]

\[= \frac{0 . 014}{1 . 515 - 1}\]

Or, \[\omega = \frac{0 . 014}{0 . 515} = 0 . 027\]

Thus, the dispersive power of the material is 0.027.