Two thin lenses are of same focal lengths f , but one is convex and...

The formula to calculate the effective focal length of the combination can be written as

$\dfrac{1}{{f}_{eff}} = \dfrac{1}{{f}_{convex}} + \dfrac{1}{{f}_{concave}} . . . \left(1\right)$

Substitute $f$ for ${f}_{convex}$ and $- f$ for ${f}_{concave}$ into equation (1) and solve to obtain the effective focal length of the combination.

$\begin{cases}\dfrac{1}{{f}_{eff}} & = & \dfrac{1}{f} - \dfrac{1}{f} \\ & = & 0 \\ & ⇒ & {f}_{eff} = \infty\end{cases}$