The refractive index of a prism with apex angle $$A$$ is $$\cot A / 2$$. The angle of minimum deviation is :

If the distance between object and its two times magnified virtual image produced by a curved mirror is $$15 \mathrm{~cm}$$, the focal length of the mirror must be:

A convex mirror of radius of curvature $$30 \mathrm{~cm}$$ forms an image that is half the size of the object. The object distance is :

A biconvex lens of refractive index 1.5 has a focal length of $$20 \mathrm{~cm}$$ in air. Its focal length when immersed in a liquid of refractive index 1.6 will be: