A biconvex lens is formed with two planoconvex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both curved surface are of the same radius of curvature R = 14 cm. For this biconvex lens, for an object distance of 40 cm, the image distance will be

A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as (Take g = 10 m/s$$^2$$)

A light beam is travelling from Region I to Region IV (Refer figure). The refractive index in Regions I, II, III and IV are $${n_0},{{{n_0}} \over 2},{{{n_0}} \over 6}$$ and $${{{n_0}} \over 8}$$, respectively. The angle of incidence $$\theta$$ for which the beam just misses entering Region IV is