Find the focal length of a convex lens of focal length $50\mathit{ cm}$ in contact with a concave lens of focal length of $40\mathit{ cm}$?

The focal length of the combination of lenses is, $200\mathit{ cm}$ and the nature of the combination is a diverging lens.
Given,
Focal length of the convex lens $= +50\mathit{ cm}$
Focal length of the concave lens $= -40\mathit{ cm}$
The focal length of the combination of lenses is calculated by
   $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$
$\Rightarrow \frac{1}{f}=\frac{1}{50}+\frac{1}{-40}$
$\Rightarrow \frac{1}{f}= -\frac{1}{200}$
$\Rightarrow$ $f= -200\mathit{ cm}$
Since the focal length is negative therefore the combination of the lens is a diverging lens of $200\mathit{ cm}$ focal length.