Why is the sign convention used in the derivation of the lens formula and yet used again when it is applied in numerical problems? Won't the whole idea of sign convention be eliminated if it is used twice?
We derive the lens or mirror formula with the sign convention. Then in solving the problem we again use sign convention to de neutralize it.
Also we use sign convention to make the calculation simple on large scale.
To identify the nature of image.
To know where is the image or object is placed with respect to lens or mirror.