The refractive index of the material of a prism is $$\sqrt 2 $$ and its refracting angle is 30^o. One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light entering the prism from the other face with retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is

A beam of light composed of red and green ray is incident obliquely at a point on the face of rectangular glass slab. When coming out on the opposite parallel face, the red green ray emerge from

An equiconvex lens is cut into two halves along (i) XOX' and (ii) YOY' as shown in the figure. Let $$f,f',$$ $$f''$$ be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively.

Choose the correct statement from the following

A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will