A container holds water up to a height of 20 cm and a point source is situated at the centre of the container's bottom. A rubber ring of radius r floats centrally on the water. The room's ceiling is 2.0 m above the water surface. Determine the maximum value of r for which the shadow of the ring is formed on the ceiling. The refractive index of water is 4/3 .

Step-by-step solution

For the shadow of the ring to be formed on the ceiling, the light rays from the point source passing just outside the ring must refract into the air and reach the ceiling. This means the angle of incidence at the water surface must be less than or equal to the critical angle _c . If the angle of incidence exceeds _c , total internal reflection occurs and no light escapes to illuminate the ceiling outside the ring. The critical angle is given by: _c = 1 = 1 4/3 = 3 4 From the geometry of the container, the maximum r