If a spherical mirror is immersed in water, does its focal length change?
Mirrors, spherical or otherwise, operate on the principle that the angle of reflection of a
ray of light equals the angle at which it strikes the mirror's surface. 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.
If you had asked about the focal length of a LENS, however, the answer would be different.
Lenses work by REFRACTION, not reflection, and the angle of refraction is based on the
difference between the speed of light in the lens compared to the surrounding medium. When
immersed in water, the difference between light's speed in the lens and the surrounding medium
is less than the difference when it's in air, and the focal length of a lens would be greater under water.
Paul Walorski, Part Time Physics Instructor
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Richard Phillips Feynman