Question

Prism angle of glass prism is 10°. It's refractive index of red and violet colour is 1.51 and 1.52 respectively. Then its dispersive power will be .

• A. 0.015
• B. 0.020
• C. 0.011
• D. 0.019

Answer 1

Answer: (D)

0.019

Answer 2

The dispersive power ($\omega$) of a prism material is defined as the ratio of its angular dispersion to the mean deviation.

The formula for dispersive power is given by: $\omega = \frac{\mu_v - \mu_r}{\mu_y - 1}$ where: $\mu_v$ is the refractive index for violet light. $\mu_r$ is the refractive index for red light. $\mu_y$ is the refractive index for yellow (mean) light.

Given values: Refractive index for red colour, $\mu_r = 1.51$ Refractive index for violet colour, $\mu_v = 1.52$ Prism angle, $A = 10^\circ$ (This is not required for calculating dispersive power, as dispersive power is an intrinsic property of the material and is independent of the prism angle for thin prisms).

First, calculate the difference in refractive indices for violet and red light: $\mu_v - \mu_r = 1.52 - 1.51 = 0.01$

Next, calculate the mean refractive index ($\mu_y$). Since the refractive index for yellow light is not given, we approximate it as the average of the refractive indices for red and violet light: $\mu_y = \frac{\mu_r + \mu_v}{2} = \frac{1.51 + 1.52}{2} = \frac{3.03}{2} = 1.515$

Now, substitute these values into the formula for dispersive power: $\omega = \frac{0.01}{1.515 - 1}$ $\omega = \frac{0.01}{0.515}$

Calculate the value: $\omega \approx 0.019417$

Rounding to three decimal places, the dispersive power $\omega \approx 0.019$.