What is the focal length of a convex lens of focal length $30 \, cm$ in contact with a concave lens of focal length $20 \, cm$? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

(N/A) Focal length of the convex lens,$f_{1} = 30 \, cm$.
Focal length of the concave lens,$f_{2} = -20 \, cm$.
Let the focal length of the system of lenses be $f$.
The equivalent focal length of a system of two thin lenses in contact is given by the formula:
$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$
Substituting the values:
$\frac{1}{f} = \frac{1}{30} + \frac{1}{-20} = \frac{2 - 3}{60} = -\frac{1}{60} \, cm^{-1}$.
Therefore,$f = -60 \, cm$.
The negative sign indicates that the system of lenses acts as a diverging lens.