Please have a look at the Lens makers formula.
In any derivation of Geometrical optics, we use the sign convention twice: once while deriving it and next while using it for general cases.
But in the derivation of lens makers formula, we don't consider negative and positive values of the radius of curvature while solving for both spherical surfaces.
This should lead to a wrong answer and in fact I solved one example which through individual analysis of both spherical surfaces gave a different answer than while using the lens makers formula directly.
I think am not getting this.
From what I have read, it's because no matter which surface light hits first the net refraction is same. This sign convention doesn't play a major role. But I am still confused.
Best Answer
I have a better explaination. You see we have used the formula for refraction on spherical surface $$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$$ in the derivation of lens makers formula. Now, the use of sign convention in any derivation is only to make the formula generalized. If we don't use sign convention, we can use the the derived formula in only the situation which we considered while deriving it. And since we have already used sign convention in the derivation of formula for refraction through spherical surfaces, we don't have to use it again in derivation of lens makers formula.