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:

If the refractive index of the material of a prism is $$\cot \left(\frac{A}{2}\right)$$, where $$A$$ is the angle of prism then the angle of minimum deviation will be