Optics: Applying Sign Conventions Twice?

[Nikhil_kumar]

Please provide me with some help in optics. This doubt is in relation to the use of sign conventions in optics. Whenever we prove anything in optics, say for example, when we prove the mirror formula or the lens formula or the lens-maker's formula, we apply the sign conventions in the derivation of the proof itself (u=-ve, f=+ve or -ve etc., according to the New Cartesian Conventions). Then while solving problems based on these formulae, why do we again have to apply the sign conventions according to the data given in the question? I mean, to solve problems based on the lens formula , the mirror formula etc. why do we have to apply the conventions twice? After all the conventions have already been applied during the course of proof itself.

For eg, The lens formula: 1/f=1/v - 1/u is derived in case of real image by convex lens by putting u=-ve, f=+ve v=+ve during the course of proof itself.

 

[rl.bhat]

In lens or mirror we get two types of images. The formula is derived for both. While solving the problems, we have apply the sign convention again to take into account the nature of the image.