Sounds like a simple problem, but I have no training in optics: I need to work out the optimal radius to use for all four surfaces of a double equiconvex lens, so that a point light source close to the surface of the back face (bfl⋝0) projects collimated light from the front face.
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Get thee to a textbook! THere is no optimal radius, really, as a setup like this will go non-spherical quickly. – Carl Witthoft Jul 16 '15 at 12:39
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I'm... not sure I know what that even means. Surely, to be parallel after passing through two symmetrical lenses from a point light source, there must be a radius which all four surfaces must have. And, I've looked around, but even though I thought it was quite straightforward, I couldn't find what I was after. – tryblinking Jul 18 '15 at 10:15
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Well... first off, spherical surfaces always have aberrations, because it takes a parabolic surface to produce perfect focussing of a parallel bundle of light rays (geometric only). So in the general case of reasonably large apertures, you need aspheric surfaces. Next, a single plano-convex lens will bring parallel light to a focus. The use of a biconvex lens pair just allows for some added corrections. Just draw the principal rays of the system. – Carl Witthoft Jul 18 '15 at 11:17
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As far as I could see, even a near-spherical parabolic lens wouldn't have a focus as close to the back surface as I might need (as my material has n=1.49), which is why I thought splitting the amount of focusing over two lenses would work best. – tryblinking Jul 18 '15 at 13:14