Question

What is the formula for dispersive power?

Answer 1

Step 1: Definitions

1. Dispersive power is defined as the power present in a transparent medium, in which the separation of light occurs due to refraction.
2. Angular separation is defined as the rate of change of angle of deviation with respect to its wavelength.
3. The angle of deviation is defined as the total difference in the angle between the incident ray and the emergence ray after refraction.
4. An emergence ray is a ray that refracts out twice from a medium.

Step 2: Formula for dispersive power

The formula for dispersive power is given as,

$\omega =\frac{\theta }{\delta }$

where $\theta$ is the angular dispersion, and $\delta$ is the mean deviation,

The angular separation between violet and red wavelength is called angular dispersion.

$\therefore \theta ={\delta }_v-{\delta }_r$

where ${\delta }_v$ is the deviation of violet light and ${\delta }_r$ is the deviation of red light.

Hence, the dispersive power can be written as $\omega =\frac{{\delta }_v-{\delta }_r}{\delta }$.