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I guess, for a convex lens I might say that the marginal rays travel a longer path but spend a shorter time inside the lens, while the opposite of that happens in case of paraxial rays. That can be an explanation for the same optical path, but what about a concave lens? For a concave lens, the marginal rays actually travel a longer path and also spend more time inside the lens. I might be wrong in my conjecture, and even if I'm right, I'd like a quantitative explanation.

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  • $\begingroup$ Intersting to note that all rays take the same time to reach a common focus point. $\endgroup$ Dec 8 '18 at 0:04
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on a concave lense you have to measure the path from the source to the virtual image, not the real image. As you can see here:

Path A is longuer than C and C is longuer than B.

enter image description here

And accordingly the lens is thicker for B than C, and thicker for C than A.

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  • $\begingroup$ May I ask for a quantitative discussion? $\endgroup$ Dec 8 '18 at 5:09
  • $\begingroup$ I may if first you find the quantitative discussion for convex lenses. $\endgroup$ Dec 8 '18 at 6:16

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