The convex surface of a plano-convex lens has an absolute value of radius of curvature of \(40 \mathrm{~mm}\). The index of refraction for the glass of which the lens is made is 1. 5 .

(a) What is the focal length of the lens?

(b) You take some measurements and determine that the \(40-\mathrm{mm}\) radius of curvature is correct but the focal length is \(100 \mathrm{~mm}\) instead of the value calculated in part \(a\). What must the index of refraction for the glass be?