Help with Optics Doubt: Sign Conventions in Problems

[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.

 

[member 553083]

Now while solving a problem based on this formula, why do we again have to apply the sign conventions according to the data given in the question? The sign conventions used in the proof of the lens formula are used to denote the positions of the object and image from the lens. That is, it is used to describe the geometry of the particular situation being considered. When solving problems based on the lens formula, the data given in the problem might include a different geometry than the one used in the proof of the lens formula. Therefore, the sign conventions must be applied according to the data given in the problem in order to correctly determine the positions of the object and image relative to the lens.