Question

Why do we apply sign convention twice in lens, one time in the formula itself and also in the problems?Clear explanation required...

Answer 1

Each time sign convention is applied, it has some purpose.

1. The first time when sign convention is applied to derive Lens Formula, it is to make sure the formula is as general as possible. Meaning you may start deriving the formula for Convex lens but since you have ensured correct sign convention is used, it turns out the formula is valid for Concave lens too.

2. Now while solving a numerical problem, you have to use the same general lens formula. Now tell me since the formula is valid for Convex and Concave lens, then how you gonna tell the formula that "Hey lens formula, I am using Convex lens, so act accordingly" ? That is where you need to apply the sign convention again in order to make sure the formula do not act weird and produce result which you don't want to.