Is the focal length of a spherical mirror affected by the medium in which it is immersed? …. of a thin lens? What’s the difference?

Mirrors

A spherical mirror may be either convex or concave. In either case, the focal length for a spherical mirror is one-half the radius of curvature.

The formula for focal length of a mirror is independent of the refractive index of the medium:

Lens

The thin lens equation, including the refractive index of the surrounding material (“air”):

The effect of the refractive index of the surrounding material can be summarized as follows:

• The focal length is inversely proportional to the refractive index of the lens minus the refractive index of the surrounding medium.
• As the refractive index of the surrounding medium increases, the focal length also increases.
• If the refractive index of the surrounding medium is larger than the refractive index of the thick lens, the incident ray will diverge upon exiting the lens.