Question

How is the focal length of a spherical mirror affected when the wavelength of the light used is increased and when it is immersed in a liquid?

Answer 1

focal length of mirror is depends only on radius of curvature

R=2f
f=R/2

The focal length does not depend upon the wavelength or the frequency so it remains unaffected.

That behavior is not affected by the medium in which the light travels, so the mirror's focal length would be no different in air or water