Optical System: Two Identical Lenses w/2fo Focal Length

[zheng89120]

Homework Statement

An optical system consists of two identical lenses; the focal length of each lens is f_o (where f_o) is positive). The lenses are separted by a distance d. Denote the focal lenths of the lens assembly by f and f'.

a) Show that for any separation of the lenses f = f'

b) Find the separation between lenses that leads to the focal length of the lens assembly being equal to 2f_o

Homework Equations

thin lens equations, refracting/travelling matrices?, f' = -1/a₂₁

The Attempt at a Solution

a) I did the intuitive approach: a set of rays coming from either end of the 2 lense assembly will experience the same assembly, and hence converge to the same focal lengths (after exiting assembly at either end)

b) I used the matrix method with the matrix for thin lense being (1, 0; -1/f_o, 1)
anyways, after some calculation... I got: d = (3/2)f_o (correct?)

 

[nickjer]

Not sure about the matrices but you could also use the formula for the focal length of compound lenses:

$$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1 f_2}$$

That will get you the same answer that you got for (b), so both methods get you the same answer. So I'd say (b) looks correct.