Find image distance

Question

A convex mirror (f1 = −6.30 cm) and a concave mirror (f2 = 9.50 cm) are facing each other and are separated by a distance of 24.0 cm. An object is placed between the mirrors and is 12 cm from each mirror. Consider the light from the object that reflects first from the convex mirror and then from the concave mirror. What is the distance of the image (di2) produced by the concave mirror?

Answer 1

Use the mirror equation for the convex mirror: 1/o1 + 1/d1 = 1/(-6.30) with o1 = 12. Solve for d1: d1 = -4.1, i.e.

the image is behind the convex mirror. This image acts as an object for the concave mirror.

The object distance o2 = 24 + 4.1 (remember the image d1 is behind the convex mirror).

Now use the mirror equation for the concave mirror

1/o2 + 1/d2 = 1/9.50.

Solve for d2.