When a butterfly of body length 4.2 cm is 10 cm from a concave mirror, its image is 15 cm behind the mirror.

The key to this type of question is the lens equation which is usually written as:

1/p + 1/q = 1/f where p is the object distance , q is the image distance and f is the focal length.

In this problem p = 10 cm, q = - 15 (negative because the image is a virtual image behind the mirror).

So 1/10 - 1/15 = 1/f . Solving for f yields f = 30 cm. The magnification , M, is =- q/p = 1.5, so the image of the butterfly will be upright = 6.3 cm.