A pole of length 1.00 m stands half dipped in a swimming pool with water level 50.0 cm higher than the bed. The refractive index of water is 1.33 and sunlight is coming at an angle of 45° with the vertical. Find the length of the shadow of the pole on the bed.

81.5 cm

Length of the pole= AB= 1m

Half of the length of the pole is under water and half is above the water surface. The point A of the pole is above the water and the light ray will first strike the water surface at the angle 45° normal to the surface and then the light rays will refract into the surface. The angle of refraction is r.

Now, the shadow length BA’ = BD + A’D = 0.5 + 0.5 tan r

Now using Snell’s law,

So, shadow length = (0.5) (1 + 0.6235) = 81.2 cm