A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of 30° with the surface of water. If swimming pool is filled to a height of 1.5 m, then the height of the pole above the water surface in centimeters is (…

Question

A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of 30° with the surface of water. If swimming pool is filled to a height of 1.5 m, then the height of the pole above the water surface in centimeters is (n_w = 4/3) .

Accepted Answer

50. Angle of incidence = 60°. In water sin r = (sin 60°)/(4/3) = (3√3)/8 ≈ 0.650, so tan r ≈ 0.854. Let h be the height above water. The ray grazing the top of the pole meets the water at a horizontal distance h cot 30° = √3h from the pole. Inside the water the ray moves a further 1.5 tan r ≈ 1.281 m sideways. √3h+1.281 = 2.15, so h ≈ 0.50 m = 50 cm. → 50

Step-by-step solution