A small bulb is placed at the bottom of a tank containing water to a depth of 7 m . The refractive index of water is 4 3 . The area of the surface of water through which light from the bulb can emerge out is x π m 2 . The value of x is _____ .

Step-by-step solution

Apply Snell's law, sin ⁡ 90 ° sin ⁡ C = μ ⇒ sin C = 1 μ ⇒ R R 2 + h 2 = 3 4 Squaring, 16 R 2 = 9 R 2 + 9 h 2 ⇒ 7 R 2 = 9 h 2 ⇒ R = 3 7 h = 3 7 × 7 = 3   m The area of the circle is, A = π R 2 = π 3 2   m 2 ⇒ α = 9