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In most lf textbooks formulas of geometric optics like lens maker formula and base formula for that are proven (or rather verified from my point of view) by taking specific case (ray diagram) and formulate equation and stated that works for all cases because we use sign convention. Why?

Here is link for that what i mean by sign convention www.tutorvista.com/content/science/science-ii/reflection-

image.wistatutor.com/content/refraction-light/lens-sign-c

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  • $\begingroup$ "Sign convention?" Can you be a bit more descriptive in your question? I would probably want to show a couple of constructions for positive and negative focal lengths, rather than wave my hands. Do you have an example of such a "proof"? $\endgroup$ – Floris Jul 29 '15 at 18:57
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    $\begingroup$ Does because it explains what we actually observe count as a reason why? $\endgroup$ – Kyle Kanos Jul 29 '15 at 19:13
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    $\begingroup$ If I'm not mistaken, the OP wants to know how one can use snell's law and some geometry to demonstrate that provided one uses certain sign conventions, one can predict e.g. image distances using the lens equation. I'm confident that someone can recommend a reference on geometric optics that does this sort of thing in detail. $\endgroup$ – joshphysics Jul 29 '15 at 19:23
  • $\begingroup$ @joshphysics you mean like en.wikipedia.org/wiki/Geometrical_optics and references therein? :-). Or, of course, Smith, "Modern OPtical Engineering" $\endgroup$ – Carl Witthoft Jul 30 '15 at 12:20
  • $\begingroup$ @joshphysics yah that, Optics Geometrical optics, or ray optics, describes light propagation in terms of rays $\endgroup$ – Vaibhav Patel Jul 30 '15 at 13:37

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