Keplerian beam expander output diameter?

In summary, the problem involves drawing the path of two parallel incident rays in a beam expander composed of two converging thin lenses with given focal lengths. The task is to prove that the outgoing beam diameter is equal to (f1/f2)*d, where d is the distance between the parallel rays and f1 and f2 are the focal lengths of the two lenses. The solution involves using the equations 1/s+1/s'=1/f and m=-s'/s, as well as the concept of similarity between isosceles triangles.
  • #1
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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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  • #2
Anyone?
 
  • #3
Use similarity.

ehild
 
  • #4
I thought about it and I still don't know how to do it.
 
  • #5
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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FAQ: Keplerian beam expander output diameter?

What is the purpose of a Keplerian beam expander?

A Keplerian beam expander is used to increase the diameter of a laser beam while maintaining its collimation, or parallel nature. This is useful for applications such as laser cutting, machining, and medical procedures.

How does a Keplerian beam expander work?

A Keplerian beam expander consists of two lenses, with the first lens having a shorter focal length than the second lens. The first lens converges the laser beam, while the second lens diverges it, resulting in a larger output diameter.

What is the difference between a Keplerian beam expander and a Galilean beam expander?

While both types of beam expanders use two lenses, a Keplerian beam expander has a converging lens followed by a diverging lens, while a Galilean beam expander has a diverging lens followed by a converging lens. This results in different output beam properties, with a Keplerian beam expander producing a collimated beam and a Galilean beam expander producing a diverging beam.

How is the output diameter of a Keplerian beam expander determined?

The output diameter of a Keplerian beam expander is determined by the ratio of the focal lengths of the two lenses. The larger the ratio, the larger the output diameter will be.

What are the limitations of a Keplerian beam expander?

One limitation of a Keplerian beam expander is that the output beam diameter is limited by the size of the lenses used. Additionally, the quality of the output beam is dependent on the quality of the lenses, and any imperfections or misalignments can affect the output beam properties.

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