A ray of light incidents at an angle of $60^{\circ}$ on the first face of a prism. The angle of the prism is $30^{\circ}$ and its second face is silvered. If the light ray inside the prism retraces its path after reflection from the second face, then the refractive index of the material of the prism is

When an object is placed infront of a convex mirror at a distance ' $u$ ' from the pole of the mirror such that the size of the image is ' $n$ ' times that of the object. Then, the object distance ' $u=$

The ratio of the focal lengths of a convex lens when kept in air and when it is immersed in a liquid is $1: 2$. If the refractive index of the material of the lens is 1.5 , then the refractive index of the liquid is

If the least distance of distinct vision for a boy is 35 cm , then the lens to be used by the boy for correcting the defect of his eye is