Keplerian beam expander output diameter?

[cdotter]

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.

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.

 

[cdotter]

Anyone?

 

[ehild]

Use similarity.

ehild

 

[cdotter]

I thought about it and I still don't know how to do it.

 

[ehild]

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