Keplerian beam expander output diameter?

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Homework Help Overview

The problem involves analyzing the path of two parallel rays in a beam expander consisting of two converging thin lenses, with the focal lengths of the lenses specified as f1 and f2, where f1 is less than f2. The task is to demonstrate that the outgoing beam diameter is proportional to the incoming beam diameter by a factor of (f1/f2).

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the correctness of the ray diagram and express uncertainty about how to begin the proof. Some suggest using similarity in triangles to approach the problem.

Discussion Status

There is ongoing exploration of the problem, with some participants offering guidance on using geometric similarity. However, explicit consensus or resolution has not been reached, as some participants continue to express confusion about the proof.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. The original poster has indicated a lack of clarity on how to proceed with the proof.

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Homework Statement



Draw the path of two parallel incident rays in a beam expander composed of two convering thin lens, with the first lens having a focal length less than the second one (f1 < f2.)

Kind of what the problem looked like.

TT48_Fig3.25.jpg


The distances between the two parallel rays (the beam diameter) was given as d. Prove that the outgoing beam diameter is (f1/f2)*d (given.)

Homework Equations


1/s+1/s'=1/f
m=-s'/s

The Attempt at a Solution



I had the ray diagram correct but I have no idea how to begin proving it. :confused:
 
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Anyone?
 
Use similarity.

ehild
 
I thought about it and I still don't know how to do it.
 
You know that those rays which travel through the focus will be parallel with the axis after traversing the lens.

See the blue and red isosceles triangles in the picture. They are similar.

ehild
 

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