A converging lens has a focal length of $10 \mathrm{cm}$ in air. It is made of a material of refractive index $1.6.$ If it is immersed in a liquid of refractive index $1.3,$ find its new focal length.

A ray of light incident normally on one face of a right angled isosceles prism is found to be totally reflected Fig. $13.77$. What is the minimum value of the refractive index of the material of the prism? When the prism is immersed in water, trace the path of the emergent ray for the same incident ray, indicating values of all the angles. $\left({\mu }_w=\frac{4}{3}\right)$.