

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 mirrors surface. That behavior is not affected by the medium in which the light travels, so the mirrors focal length would be no different in air, glycerine or water. However, the lenses work by refraction, not reflection. Hence, the angle of refraction is based on the difference between the speeds of light in the lens compared to the surrounding medium. When immersed in glycerine, the difference between lights speed in the lens and the surrounding medium is less than the difference when its in air and the focal length of a lens would be greater under glycerine.
