A Double-Convex Thin Glass Lens Has Equal-Magnitude Radii of Curvature $+ 31.2 \mathrm {~cm}$

Multiple Choice

A double-convex thin glass lens has equal-magnitude radii of curvature. The focal length of this lens is $+ 31.2 \mathrm {~cm}$ and the index of refraction of the glass is $1.52$ . The lens is to be replaced with a plano-convex glass lens of the same focal length and thickness. The radius of curvature of the convex surface of the replacement lens is $13.0 \mathrm {~cm}$ . What should be the index of refraction of the glass of the plano-convex lens?

A) $1.40$
B) $1.42$
C) $1.38$
D) $1.36$
E) $1.44$