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1. While deriving the lens formula for a convex lens-say, 1/f= 1/v - 1/u where u and v are the object and image distances, the minus sign is obtained after applying sign conventions. But, I don't understand the logic behind taking the value of u again with a minus sign and substituting in the formula while solving problems.For example, if the object distance is given as 45 cm and the image distance as 90 cm we again apply the sign convention, take u as -45 cm and substitute in the above formula and calculate f as 30 cm. In fact, while doing so the above formula becomes 1/f = 1/v + 1/u. What is the meaning behind applying negative sign in a formula which is itself obtained by applying the negative sign already?

2. Again, take the convex lens formula, 1/f = (n-1) (1/R1 -1/R2) where n is the refractive index and R1 and R2 are radii of the two faces of the lens. For a biconvex lens, assuming that R1 = R2, and n= 1.5 roughly for glass,then substituting these values in the above formula, we get the value of f as infinity, which is really absurd. Can any one throw light on the above points?