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

A ray of light travels from a denser medium to a rarer medium. The reflected and the refracted rays are perpendicular to each other. If '$$r$$' and '$$r_1$$' are the angle of reflection and refraction respectively and '$$\mathrm{C}$$' is the critical angle, then the angle of incidence is