Waves on a spherical refracting surface

Suppose that light is incident parallel to the optic axis

The ray coming in along the optic axis is not deflected. The ray incident at a height y above the optic axis bends as shown.

With air on the left side and glass on the right we have

This is independent of y, so all incident rays that hit the spherical surface parallel to the optic axis are refracted through F

The refracted ray intersects the optic axis at some point H

Solve for y’ and the distance VG

and we have

All the light is focused at one point, lying on a plane perpendicular to the optic axis, the so-called focal plane.

Recall that so that From the geometry,

When the external medium has a refractive index n 1, the corresponding formula is n1n1 n2n2