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 15 cm floats centrally on the water. The room's ceiling is 2.0 m above the water surface. Determine the radius of the shadow of the ring formed on the ceiling. The refractive index of water is 4/3 .

Step-by-step solution

Let the angle of incidence of the light ray at the edge of the rubber ring be i . From the geometry of the setup, we have: i = r h = 15 cm 20 cm = 3 4 This gives i = 3 5 . Applying Snell's law at the water-air interface: _ w i = _ a r' 4 3 3 5 = 1 r' r' = 4 5 r' = 4 3 The light ray emerges into the air at an angle r' and travels to the ceiling, which is at a height H = 2.0 m above the water surface. The additional horizontal distance traveled by the ray in the air is: x = H r' = 2.0 4 3 = 8 3 m 2.667 m The total ra