One of the necessary condition for total internal reflection to take place is

( $$\mathrm{i}=$$ angle of incidence, $$\mathrm{i}_{\mathrm{c}}=$$ critical angle)

A double convex lens of focal length '$$F$$' is cut into two equal parts along the vertical axis. The focal length of each part will be

The size of the real image produced by a convex lens of focal length $$F$$ is '$$m$$' times the size of the object. The image distance from the lens is

The prism has refracting angle '$$\mathrm{A}$$'. The second refracting surface of the prism is silvered. Light ray falling on first refracting surface with angle of incidence '$$2 \mathrm{~A}$$', reaches the second surface and returns back through the same path due to reflection at the silvered surface. The refractive index of the material of the prism is