A diverging lens with f = -32.5 cm is placed 15.0 cm behind a converging lens with f = 21.0 cm .?

Question

Where will an object at infinity be focused? Determine the image distance from the second lens. Follow the sign conventions.

Answer 1

Consider an object in front of a diverging lens.  Where is the image?  On the same side as the object but closer to the lens.  Now find the image from the first ( convex ) lens.  the image is at f = 21 cm from the lens or 6 cm to the right of the concave lens. So you know that the image of that will be less than 6cm but also to the right of the concave lens.

1/do + 1/di = 1/f    -> 1/di = 1/f - 1/do  -> di = 1/(1/-32.5 - 1/6) = -5.06 cm

ie 5.06 cm to the right of the concave lens.