Question

Directions: The following question has four choices, out of which one or more are correct.A ray of light is incident on a reflecting surface. The ray moves in horizontal direction and is reflected vertically after striking the surface. If the surface is denoted by y=2Lπsin⁡(πLx),0≤x≤L, what are the coordinates of the point(s) where the ray is incident?

• A. (A) (L4,2Lπ)
• B. (B) (L3,3Lπ)
• C. (C) (3L4,2Lπ)
• D. (D) (2L3,3Lπ)

Answer 1

Answer: (A), (D)

(A) (L4,2Lπ)

Answer 2

Explanation:
Consider the diagram for reflection at general point A shown below.Here, we have.2i=90∘i=45∘So, dy/dx at A should be tan⁡45∘. Thereforey=2Lπsin⁡(πLx)dydx=2Lπcos⁡(πLx)×πL1=2cos⁡(πLx)πxL=π3x=L3Therefore,y=2Lπsin⁡(πL×L3)=2Lπ×32=3LπTherefore, the point is (L3,3Lπ). Another point, just opposite on the surface will also act same and its coordinates are (2L3,3Lπ)