Dispersive power is a measure of the ability of a material to separate different colors of light.

Dispersive power formula:
The formula for dispersive power is given by the equation:

Dispersive power = angular dispersion / mean deviation

Let's understand each term in this formula:

1. Angular dispersion:
Angular dispersion is defined as the difference in deviation of different colors of light produced by a prism. When a beam of white light passes through a prism, it gets separated into its constituent colors due to different refractive indices for different wavelengths. The angular dispersion is the angular separation between the extreme violet and extreme red rays after passing through the prism.

2. Mean deviation:
Mean deviation is a measure of the average deviation of different colors of light produced by a prism. It is calculated by taking the average of the deviations of different colors from their mean position.

3. Dispersive power:
Dispersive power is a quantitative measure of the ability of a material to disperse light. It indicates how effectively a material can separate different colors of light. The higher the dispersive power, the greater the ability of the material to separate the colors of light.

Explanation of the formula:
The formula for dispersive power states that dispersive power is equal to the ratio of angular dispersion to mean deviation. This formula can be derived from the relationship between angular dispersion and mean deviation.

When light passes through a prism, the different colors are refracted at different angles due to their different wavelengths. This causes the light to spread out, forming a spectrum. The angular dispersion is the angular separation between the extreme violet and extreme red rays in this spectrum.

On the other hand, the mean deviation is a measure of the average deviation of the different colors from their mean position. It represents the average angular deviation of the different colors from their initial direction.

The dispersive power is then calculated as the ratio of angular dispersion to mean deviation. This ratio gives us a measure of how much the light is dispersed or separated by the prism. A higher dispersive power indicates a greater ability of the material to separate the different colors of light.

Therefore, option 'D' is the correct formula for dispersive power.