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Currently I'm trying to create a sniper rifle scope, and would like to create a magnified scope effect (with modeled lenses if necessary). But I'd like to make this a more general question, as that would be more useful.

If I have a magnifying glass, or a gun scope, or a telescope, and I want to turn it into a magnifying lens, what's the best way to go about it in Cycles?

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The Glass BDSF material in the Cycles renderer does this quite nicely. The controlling variable is the IOR (index of Refraction). Set it to 1.0 and the lens will act like it is made of air (no effect, in essence). Keep it at the default 1.45 and apply the material to a lens-shaped object, and you should see the effect you are looking for. Play around with IOR until you get what you need.

my example

Carlo's example

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    $\begingroup$ Nicely answered. I'll add something - for anyone wanting only the refraction and not the gloss or any change in color values, use a Refraction BSDF instead of a Glass BSDF. This can be useful if you're modeling a fisheye lens to go in front of your camera or something like that. $\endgroup$ – Mentalist Sep 8 '15 at 2:59

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