Image Formation (Convex-Convex lenses)

Question

I'm given with these data:

Lens 1 and lens 2 are convex lenses with different focal lengths

Distance of object from lens 1: 50 mm
Distance between lens 1 and lens 2: 100 mm
Distance of final image from lens 1: 300 mm

How to compute for the Distance of first image from lens 1? A ray diagram for this kind of set-up will be appreciated.

Answer 1

You just use the lens formula:

$$ \frac{1}{u} + \frac{1}{v} = \frac{1}{f} $$

Do the calculation for the first lens to find the position of the image, then do the calculation for the second lens taking $u$ to the distance of the first image from the second lens. Make $u$ negative if the image is on the far side of the second lens.