Finding image distance?

Question

Two identical diverging lenses are separated by 20 cm. The focal length of each lens is -13 cm. An object is located 4.5 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.

thank u

Answer 1

v = distance of 1st image from 1st lens.

w = distance of 2nd image from 2nd lens.

Real is positive sign convention.

1 / 4.5 + 1 / v = - 1 / 13

v = - 3.34 cm.

That is a virtual image 3.34 cm. left of the first lens.

Its distance from the second lens is:

3.34 + 20

= 23.34 cm.

A virtual image has real light appearing to diverge from it, and it is therefore a real object for the second lens.

1 / 23.34 + 1 / w = - 1 / 13

w = - 8.35 cm.

That is a virtual inage 8.35 cm. left of the second lens.