A vessel is fully filled with liquid having refractive index $\frac{5 }{3}$. At the bottom of the vessel a point-like source of light is kept. An observer looks at the source of light from the top. Now, an opaque circular disc is kept on the surface of the water in such a way that its centre just rests above the light source. Now liquid is taken from the bottom gradually . Calculate the maximum height of the liquid to be kept so that light source cannot be seen from outside. (Radius of the disc is 1 cm.)

The radii of curvature of a convex lens are 10 cm and 15 cm. If its focal length is 12 cm. The refractive index of the material of the lens = _____ .

The focal length of a convex lens in air is 20 cm. What will be its focal length in water ? (The refractive index of water is 1.33 and that of glass is 1.5.)