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. 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 σ , the angular extent δ of the imag

Step-by-step solution

In trapezium O E C B , the sides O E ∥ C B and the angles are shown in the figure below: x = 90 ° - u - α y = 90 ° - v - α ∠ O P B = ∠ E P C ∠ O P E = ∠ B O C which gives, 90 ° - u - α = 90 ° - v - α ⇒ u = v ∠ O P E + ∠ E P C = 180 ° 180 ° - x + y + 180 - 2 v - δ = 180 ° - 180 ° - u - v - 2 α + 180 ° - 2 v - δ = 0 ( u = v ) ⇒ δ = 2 α .