# Homework Help: Laser beam spreader optics problem

1. Sep 11, 2007

### ice109

1. The problem statement, all variables and given/known data
Two positive lens are to be used as a laserbeam expander. An axial 1mm diameter beam enteres a short focal length positive lens, which is followed by a somewhat longer focal length positive lens from which it emerges with a diameter of 8mm. Given that that first lens has a 50mm focal length determine the focal length of the second lens and the seperation between them.

2. Relevant equations
$$\frac{1}{s_o_1}+\frac{1}{s_i_1}=\frac{1}{f}$$
$$M=\frac{-s_i_1}{s_o_1}(\frac{-s_i_2}{s_o_2})$$

3. The attempt at a solution
well if the object is at infinity, which a collimated beam, a laser, would look like, then it converges to the focus on the other side of the thins lens. But this yields a zero magnification. I can draw a ray diagram after that rays converge to the focus and continue past it they diverge again and if the point they diverge from is the focus of the second lens they will come out collimated again. The problem is that neither of those two equations really describe anything about that. So i can make the ray diagram look right but not the math.

the problem is that theres a bunch of infinities floating around and i don't know how to work with them. in another problem in the book they actually cancled an infinity over an infinity which of course makes no sense to me.

Last edited: Sep 11, 2007