Question

A 4.9-m-wide swimming pool is filled to the top. The bottom of the pool becomes completely shaded in the afternoon when the sun is 22 ∘ above the horizon.

Answer 1

the width of the swimming pool = 4.9 m  

the angle made by the sun ray with horizon = 22

consider the depth of the swimming pool is " d " m.

According to Snell"s law n₁ sin i = n₂ sin r

where, n₁ = refractive index of air = 1 ,

n₂ = refractive index of water = 1.33

  i = angle of incidence =68 ( 90 - 22 ) ,

therefore 1 x sin 68 = ( 1.33 ) sin r

              sin r = sin 68 / 1.33   = 0.927 / 1.33 = 0.697

sin r = 0.697

r = sin^-1 (0.697 ) = 44.197

SInce,  tan r = width of the swimming pool / depth of the swimming pool

depth of the swimming pool , d = 4.9 x tan (44.197)

                                                                      = 4.9 x 0.972

                                                                      = 4.76 m

                                                                      = 5 m ( approximately )

Therefore the depth of the swimming pool is 5 m.