A small piece of wood floats on the surface of a 2.5 m deep lake. Determine the position where the shadow forms on the bottom when the sun is just setting. The refractive index of water is 4/3 .

Step-by-step solution

When the sun is just setting, the angle of incidence of the light rays is i = 90^ . Using Snell's law: (90^ ) = (r) 1 = 4 3 (r) (r) = 3 4 The tangent of the angle of refraction is: (r) = (r) 1 - ^2(r) = 3/4 1 - (3/4)^2 = 3 7 The horizontal shift of the shadow from the position directly below the piece of wood is: x = h (r) Substituting h = 2.5 m : x = 2.5 3 7 = 7.5 7 Using 7 2.645 : x 7.5 2.645 2.83 m