Question

If a virtual image is formed along the principal axis 10 cm from a concave mirror with focal length 15 cm what is the object distance from the mirror

Answer 1

Let $d$ be the distance from the object to the mirror, $f$ be the distance from image to the mirror and $F$ be the focal length. The relation between these parameters is (for the virtual image)

$\dfrac1d -\dfrac1f = \dfrac1F.$ So $\dfrac1d = \dfrac1f + \dfrac1F = \dfrac{1}{10} + \dfrac{1}{15} = \dfrac16.$ Therefore, $d=6\,\mathrm{cm}.$