An Introduction to Modern Astrophysics · Problem 6.3

Binary Systems and Stellar Parameters — Carroll & Ostlie

Physics — Astrophysics · combined-focal-length

Problem

Show that if two lenses of focal lengths

f_1

and

f_2

can be considered to have zero physical separation, then the effective focal length of the combination of lenses is

\frac{1}{f_{\mathrm{eff}}} = \frac{1}{f_1} + \frac{1}{f_2}.

Note: Assuming that the actual physical separation of the lenses is

x

, this approximation is strictly valid only when

f_1 \gg x

and

f_2 \gg x