Two thin lenses of focal length \(f_1\) and \(f_2\) are placed in contact with each other coaxially. Prove that the focal length \(f\) of the combination is given by
\[
f=\frac{f_1f_2}{f_1+f_2}.
\]
Show Hint
For lenses in contact:
\[
P=P_1+P_2
\]
or
\[
\frac1f=\frac1{f_1}+\frac1{f_2}.
\]
Always remember that powers add directly whereas focal lengths do not.