$1.$ A doublet is constructed using an equiconvex thin lens placed in intimate contact with a diverging thin lens such that the combination will have focal length of $30$ cm in air. If their indices are $1\mathrm{.}5$ and $1\mathrm{.}49,$ respectively, determine all radii of curvature of the surfaces of the two lenses given that focal length of the diverging lens is $-30$ cm $.$