Consider a thin, spherical plano$-$convex lens having a radius of curvature of $50\mathrm{.}0$ mm and an index of $1\mathrm{.}5.$

a$)$ Determine the focal length in air.

b$)$ Suppose this lens is placed right on the surface of a tank of water. At what depth below the surface would a collimated light beam from above come to a focus? $($The refractive index of water is $\frac{4}{3}.).$