A glass cube of length $$24 \mathrm{~cm}$$ has a small air bubble trapped inside. When viewed normally from one face it is $$10 \mathrm{~cm}$$ below the surface. When viewed normally from the opposite face, its apparent distance is $$6 \mathrm{~cm}$$. The refractive index of glass is

A particle executes linear S.H.M. The mean position of oscillation is at the principal axis of a convex lens of focal length $$8 \mathrm{~cm}$$. the mean position of oscillation is at 14 cm from the lens with amplitude 1 cm. The amplitude of oscillating image of the particle is nearly

A convex lens of focal length $$\mathrm{T}$$ is used to form an image whose size is one fourth that of size of the object. Then the object distance is

Inside a vessel filled with liquid a converging lens is placed as shown in figure. The lens has focal length $$15 \mathrm{~cm}$$ when in air and has refractive index $$\frac{3}{2}$$. If the liquid has refractive index $$\frac{9}{5}$$, the focal length of lens in liquid is