A mirror produces inverted twice magnified image of an object at a distance of $$30\text{ cm}$$ from the object. Find the focal length (in cm) of the mirror.

An inverted magnified image is real, formed by a concave mirror, with image distance twice the object distance on the same side. If the object is at $$u$$, the image is at $$2u$$ and $$2u - u = 30$$, so $$u = 30\text{ cm}$$ and $$v = 60\text{ cm}$$. Then $$f = \frac{uv}{u + v} = \frac{1800}{90} = 20\text{ cm}$$ (concave).