Are Back & Front Focal Lengths Equal for Thick Lenses?

[zak8000]

Homework Statement

is the back focal length equal to the front focal length of a thick lens ie a thick plano convex lens?

i know it is not but do not know how to clarify it please help

Homework Equations

The Attempt at a Solution

 

[revacious]

A planoconvex lens is shaped like a capital D. One side has 0 power, and the other side has a power (because it has a curvature). Assume the lens has a thickness of d and a refractive index of n.

The BVP is given by (F1+F2-(d/n)F1F2)(1-(d/n)F1)
The FVP is given by (F1+F2-(d/n)F1F2)(1-(d/n)F2)

Subbing in F1 = 0, F2 = F2, we can clearly see that BVP is not the same as FVP (unless d is 0 but we disregard this, because the lens has a definite thickness).