Question

what is the power of a mirror in water (with index of refraction 1.333) , if a lens-clock (with index of refraction 1.530) measures the surface power of the mirror to be +8.5D in air (n=1)?

Answer 1

A lens clock is an instrument with three pins. Two pins at the two ends are fixed,and the third pin at the center is moving.

The central pin's movement is used to measure the curvature of the surface, and with it, the refractive power of the instrument.

The optical power of the surface is given by

Here, n is the refractive index of the glass with respect to the medium, s is the amount by which the central pin moved, and D is the separation between the outer pins.

For a fixed mirror, s and D are constants.

Only n changes when the medium changes.

At first, the medium is air.

So,

For the system immersed in water,

Here, in air,

So,