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All textbooks I've come across have the same way of proving the mirror formula. Everything makes sense, except the fact that they apply the sign convention once to obtain the mirror/lens formula, but when they use the formula to solve a question, they apply the sign convention again. Why?

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This double application of the convention adopted is fundamental to use the formula you derived to make useful predictions.

In fact, quantities involved in such demonstrations (I assume you are talking about geometrical optic, aren't you?) need a convention in order to account for the reciprocal position of two points. If you stated that some quantity is positive in a certain direction in the demonstration of a certain formula, then when it comes to apply this formula you necessarily have to use the same convention, in order to this formula to be valid and useful to make predictions (i.e., solve exercises).

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  • $\begingroup$ Yes I'm talking about Geometric Optics. Unfortunately your answer doesn't seem to clear my doubt:( $\endgroup$ – Kunal Pawar Feb 19 '17 at 16:56
  • $\begingroup$ @KunalPawar Sincerely, I don't know how to answer differently. I think your doubt is legitimate. I think it could be clearer if you try to derive the formula with one convention and apply it with another one to find out the inconsistencies it brings to. $\endgroup$ – JackI Feb 19 '17 at 17:04
  • $\begingroup$ That's kinda working backwards... I tried it once... baffled me even more. $\endgroup$ – Kunal Pawar Feb 19 '17 at 17:06
  • $\begingroup$ @KunalPawar I'm trying to think again to my answer. Maybe I have not completely understand your doubt. Could you please try to rephrase it? For me, it is just a matter of consistency in the development of a theory and in its application. $\endgroup$ – JackI Feb 19 '17 at 20:58
  • $\begingroup$ It's just that if I already applied the sign convention. Why apply it again? $\endgroup$ – Kunal Pawar Feb 20 '17 at 1:16

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