An object is placed at a distance $d = 20$ cm from a diverging lens of focal length $f = -10$ cm. Find the image distance and state what kind of image it is.
The thin lens formula:
$$\frac{1}{f} = \frac{1}{d} + \frac{1}{d'}$$
$$\frac{1}{d'} = \frac{1}{f} - \frac{1}{d} = -\frac{1}{10} - \frac{1}{20} = -\frac{3}{20}$$
$$d' = -\frac{20}{3} \approx -6.67 \text{ cm}$$
The negative value means a virtual image located in front of the lens (on the same side as the object).
$d' = -6.67$ cm — a virtual image in front of the lens