Question

Two thin converging lenses of focal length $f_1$ and $f_2$ are placed coaxially in contact. Derive expression for the focal length of the combination.

Hint:

When adding the equations for thin lenses in contact, the intermediate image term $\frac{1}{v_1}$ always cancels out nicely. This principle scales infinitely: for $n$ lenses in contact, the net focal length is simply $\frac{1}{F} = \sum \frac{1}{f_i}$.

Answer 1