The image of an object O due to reflection from the surface of a lake is elongated due to the ripples on the water surface caused by a light breeze. This is because the ripples act as tilted mirrors as shown below. Consider the case, where O and the observer E are at the same height above the surface of the lake. If the maximum angle that the ripples make with the horizontal is α , then the angular extent δ of the im

Step-by-step solution

We can consider ripples as plane mirrors reflecting light to form image with angular extent δ . It is given O and E are at same level, so O E B C is a trapezium with O E | | B C . Now, different angles of trapezium O E B C are as shown below. ∠ 1 = 90 ° - β - α ∠ 2 = 90 ° - γ - α ∠ O P B = ∠ E P C and ∠ O P E = ∠ B O C ⇒ 90 ° - β - α = 90 ° - γ - α ⇒ β = γ . . . . i As, ∠ O P C = 180 ° ⇒ 180 ° = β + γ + 2 α + 180 - 2 γ - δ ⇒ 2 α + β - γ - δ = 0 ⇒ δ = 2 α [ ∵ β = r from Eq. (i) ]