An object is placed $15$ cm in front of a concave mirror of focal length $10$ cm. Find the position and nature of the image.

Using $\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$ with $f = 10$ and $u = 15$: $\dfrac{1}{v} = \dfrac{1}{10} - \dfrac{1}{15} = \dfrac{1}{30}$, so $v = 30$ cm. A positive $v$ for a concave mirror means a real, inverted image in front of the mirror. Adding the reciprocals gives 6 cm.