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We are given $\sigma=\frac{r2+r1}{r2-r1}$, with $\sigma$ being the Coddington shape factor. What I am having problems with is solving for $r1$ and $r2$ when I am just given a focal length and a refractive index, along with $\sigma$. From the lensmaker's equation, we know that $\frac{1}{f}=(n-1)(\frac{1}{r1}-\frac{1}{r2})$, but I just can't seem to get it to come out where I can solve for just $r1$ or just $r2$. Any advise on how I should go about this?

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NightHallow, although the title of your question is great, the body sounds a lot like a homework problem. This is a site for conceptual questions, so we expect homework-like questions to focus on the specific concept that is giving you trouble. See this meta post for more information. If you can rewrite the question to be more conceptual and to focus on the part of the problem that is giving you trouble, I'd be happy to reopen it. – David Z Oct 20 '11 at 0:34
I'm sure your book mentions that the shape factor is simply the sum of the radii of curvatures divided by their difference. To find the curvatures for a lens of a given focal length, you just set up the equations for focal length and shape factor and solve them. If you need help solving a system of equations you can ask on math.SE or, if it has some physical significance, you can ask here, but you should show us what you've tried and what is stumping you. Even with your edit, your question amounts to "tell me about shape factors" which isn't really a question as much as a discussion. – Colin K Oct 20 '11 at 15:55
If you take away the first sentence, it actually seems fine, enough so that I'm okay with reopening this. (Although it could be argued that this is more of a math question than a physics question, but that's not a problem; we can always migrate it to Mathematics if necessary) – David Z Oct 20 '11 at 17:29

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