Q88 / 91 · KVPY 2018 (SB/SX) · Physics

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 image will be

Figure

  • A
    α2
  • B
    α
  • Correct answer
    C
    2α
  • D
    4α

Solution

Figure
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 OEBC is a trapezium with OE||BC.

Now, different angles of trapezium OEBC are as shown below.

Figure

∠1=90°-β-α

∠2=90°-γ-α

∠OPB=∠EPC

and ∠OPE=∠BOC

⇒90°-β-α=90°-γ-α

⇒β=γ....i

As, ∠OPC=180°

⇒180°=β+γ+2α+180-2γ-δ

⇒2α+β-γ-δ=0

⇒δ=2α  [∵β=r from Eq. (i) ]

Hence, the correct answer is option: 'C'.

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