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 )   _ _ _ _ _ _ _ _ .

Step-by-step solution

Let angle B A C is θ . Applying Snell's law at E , we get 1 × sin 60 ° = 4 3 × sin θ ⇒ sin θ = 3 3 8 ⇒ tan θ = sin θ 1 - sin θ 2 = 3 3 37 Now, B C = 1 . 5 × tan θ = 1 . 28 Then, A B = 2 . 15 - B C = 0 . 86   m Required value, D F = A B   tan 30 ° = 0 . 5015   m ≈ 50   cm