We next consider a point object O in front of a concave refracting surface SPM separating...

We next consider a point object O in front of a concave refracting surface SPM separating two media of refracting indices n1 and n2 [see Fig. 3.34]; C represents the center of curvature. In this case also one obtains a virtual image. Let Q represent an arbitrary point on the axis. We now have to consider the optical path length Lop = n1 OS – n2 SQ; show that it is given by

    (94)

Also show that the above expression leads to the paraxial image point which is consistent with Eq.(10); we may note that u,v and R are all negative quantities because they are on the left of the refracting surface.