What is dispersive power?a)The ratio of angular dispersion to the angle of deviation for the mean wavelength.b)The ratio of angular dispersion to the angle of refraction for the mean wavelength.c)The ratio of angular dispersion to the angle of reflection for the mean wavelength.d)The ratio of angular dispersion to the angle of deviation for the total wavelength.Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Dispersive power of a prism is defined as the ratio between angular dispersion to mean deviation produced by the prism.
If dμ denotes the difference between the refractive indices of material of prism for violet and red light,
ω = δμ / μ – 1
Here ‘μ’ is the refractive index of prism for a mean colour. A mean colour is that colour whose wavelength lies in between that of violet and red. For white light, yellow colour is, generally, taken to be the mean colour.
Since μv is always greater than μr, the dispersive power of a prism is always positive. It depends upon the type of glass used. It is different for crown glass and for flint glass.

Answer

Dispersive power is the measure of the ability of a material to separate different wavelengths of light. It is defined as the ratio of angular dispersion to the angle of deviation for the mean wavelength.

Explanation:

Angular Dispersion:
Angular dispersion refers to the separation of different wavelengths of light as they pass through a prism or any other dispersive medium. When white light passes through a prism, it gets refracted at different angles depending on its wavelength. This results in the formation of a spectrum of colors, with each color having a different angle of refraction. Angular dispersion is the difference in angles of refraction between two colors.

Angle of Deviation:
When light passes through a prism, it deviates from its original path due to refraction. The angle of deviation is the angle between the incident ray and the emergent ray after passing through the prism. It depends on the angle of incidence and the refractive index of the prism.

Mean Wavelength:
White light is made up of a combination of different wavelengths, each corresponding to a different color. The mean wavelength is the average of all the wavelengths present in white light.

Dispersive Power:
Dispersive power is a measure of how much a material separates different wavelengths of light. It is defined as the ratio of angular dispersion to the angle of deviation for the mean wavelength. In other words, it quantifies the amount of dispersion produced by a material for a specific range of wavelengths.

The correct answer is option 'A' because it correctly states that dispersive power is the ratio of angular dispersion to the angle of deviation for the mean wavelength. This definition accurately describes the concept of dispersive power and its relationship with angular dispersion and angle of deviation. By calculating the dispersive power, we can compare the ability of different materials to separate different wavelengths of light and understand their dispersion characteristics.

In conclusion, dispersive power is a crucial concept in the study of optics and the behavior of light. It helps us understand how different materials can separate and disperse different wavelengths of light, leading to the formation of spectra.

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