Optical Path Length: Deriving Reflected Light on Lens Surface

[kpl]

Homework Statement

Derive the optical length of the incident light being reflected back to the surface of the lens with radius r1.

Homework Equations

i have assumed that the surfaces can be given as r^2 = y^2+z^2
there are 2 surfaces of the lens with radii r1 and r2

The Attempt at a Solution

is it simply subtracting the expression for r1 from the expression for r2?
i have attemped using Fermats principle but cannot get very far

 

[n0_3sc]

I think I remember doing this problem a while back - if I'm right, the derivation is not simple. If nobody replies, give me some time to recall my memory...

 

[n0_3sc]

I don't know if you've managed to do the problem but you were on the right track.

You asked whether or not you subtract the expression for r1 from r2 - that depends if you represented the reflected light ray's velocity as negative or if you've subtracted the entire reflected path. Either way should be fine, though I would probably stick with representing the reflected velocity as negative.