Question

How is the focal length of a spherical mirror affected, when the wavelength of the light used is increased?

Answer 1

Spherical mirrors have various refractive indexes based on the wavelength of the light. In other words, the refractive index becomes lesser as the wavelength of light becomes more. Because focal length is associated with refractive index, the various wavelengths of light get focused at various points. For instance, blue light which has smaller wavelength than red light also has lesser focal length than for red light. Therefore, the focal length of a spherical mirror is increased when the wavelength of the light used is increased.

Answer 2

As light travels from one medium to another say from air into glass, the speed of light and the wavelength of the light changes but only the frequency remains constant.

When these changes occur then light is refracted in the medium. We can therefore define a relationship between the wavelength of light in the different mediums and and the refractive index of the medium where light is refracted.

Let Y represent the wavelength of light in air and Ym the wavelength of light in the spherical mirror. Let n represent the refractive index of the spherical mirror, then

n=Y/Ym

As the wavelength of light increases so does the refractive index and vice versa.

Focal length is inversely proportional to refractive index of a spherical mirror

The more the refractive index the more the rate of convergence and thus the less the focal length. So as light wavelength is increased, the focal length of the spherical mirror decreases.