Two thin lenses are of same focal lengths ($f$), but one is convex and the other one is concave. When they are

Question

Two thin lenses are of same focal lengths ($f$), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be

Accepted Answer

The equivalent focal length $F$ of two lenses in contact is given by $\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$. For a convex lens $f_1 = f$ and for a concave lens $f_2 = -f$. Thus, $\frac{1}{F} = \frac{1}{f} - \frac{1}{f} = 0$, which implies $F = \infty$.

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