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Parallel rays coming from infinity are said to meet at focal plane.I was looking for the proof of that phenomena

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    $\begingroup$ Do you mean after they pass through a converging lens? $\endgroup$ – Aaron Stevens Jul 28 '18 at 20:28
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    $\begingroup$ After they pass through a converging lens or get reflected by a concave mirror $\endgroup$ – Nayem khan Jul 28 '18 at 20:45
  • $\begingroup$ Use the ABCD matrix formalism. $\endgroup$ – wcc Jul 28 '18 at 21:19
  • $\begingroup$ I think the search term you want is "non-axial ray". And I've seen a interesting paper on the pedogogy of the subject recently (perhaps in The Physics Teacher). $\endgroup$ – dmckee Jul 28 '18 at 23:08
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    $\begingroup$ You can prove it for a spherical glass or mirror of a small curvature. You can also prove it for a parabolic mirror with a non-small curvature. A glass of a non-small curvature should be aspheric, but I am not sure of its exact shape. $\endgroup$ – safesphere Jul 28 '18 at 23:24
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you put a screen behind the lens, and you will see the light make a small spot as you move the screen. There lies your focal point.

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The proof is “by construction”: the lens, mirror or more complicated optics system was constructed to do exactly that.

Why is that useful? It maps light arriving at each particular angle to a specific point on the focal plane. Since light from different points on a distant object arrive at different angles, this lets the optical system form an image of the distant object.

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