What Happens to Parallel Rays in Compound Lens and Mirror Setups?

[mihajovics]

Homework Statement

You have a thin lens with a concave and a convex side (let's say with radii r and R). You also have 2 mirrors, a convex one, that fits perfectly into the lens' concave side, and a concave one, that fits perfectly onto the lens' convex side (so the corresponding radii of the mirrors are R and r).

Representation:
D = lens
I = mirror1
) = mirror2

position1:
ID <--- rays are coming from this side

position2:
rays are coming from this side ---> D)

Okay, it's lame, but I couldn't get a better one The lens and mirrors when attached to each other fit perfectly together, they complement one another, so there's no distance between them at all.
You could also think of the problem as spraying some silver or other metal on one side of the lens, creating a thin layer that reflects light perfectly.

The question is, what happens to the parallel rays in the two aforementioned setups?

2. Homework Equations / 3. The Attempt at a Solution

Well, the problem is I don't understand what's going on. I know general optics, the usual geometrical stuff, but can't find a useful tool for this problem from that bag of tricks.
It's kind of urgent, so thanks in advance for your help.

 

[Redbelly98]

Well, there are a few things to keep in mind, to help think about this:

1. When you have two closely-spaced lenses next to each other, what is the effective focal length of the two-lens system?

2. A mirror is like a lens with focal length f = ___?

3. With a mirror next to a lens, rays will pass through the lens twice, so effectively it is as if you have two lenses and the mirror.