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.

 

[kerimek]

Thank you for providing the homework statement and your attempt at a solution. This is a very interesting problem and it involves the concept of compound lenses and mirrors.

In the first setup, where the lens and mirrors are attached to each other, the parallel rays will first pass through the lens and then reflect off of the mirrors. The lens will refract the light and the mirrors will reflect the light, causing the rays to converge at a point behind the lens. This is known as a compound lens system, where multiple lenses and mirrors are used to manipulate light in a specific way. The exact position of the focal point will depend on the radii of the lens and mirrors and their respective distances from each other.

In the second setup, where a thin layer of reflective material is added to one side of the lens, the parallel rays will simply reflect off of the lens and converge at a point behind the lens. This is similar to a simple mirror, where the angle of incidence is equal to the angle of reflection. However, because the lens is curved, the rays will converge at a single point rather than being reflected in a single direction.

I would suggest using the thin lens equation and the mirror equation to solve this problem. These equations take into account the curvature and distance of the lens and mirrors and can help determine the position of the focal point. Additionally, understanding the concept of compound lenses and mirrors can also aid in solving this problem.

I hope this helps and good luck with your homework!