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A reflecting surface is represented by equation $Y = \frac{2 L}{π} \sin (\frac{π x}{L}), 0 \leq x \leq L$ A ray travelling horizontally becomes vertical after reflection. The $X$ coordinates of the point(s) where this ray is incident is

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$\frac{L}{3}$

$\frac{\sqrt{3} L}{π}$

$\frac{\sqrt{3} L}{4}$

$\frac{3 L}{2}$

answer is A.

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Detailed Solution

A horizontal ray becomes vertical after reflection

$\tan θ = \frac{dy}{dx} = 2 \cos \frac{πx}{L}$

$2 θ = 90^{\circ} \Rightarrow θ = 45^{\circ}$

$1 = 2 \cos (πx / L) \Rightarrow x = L / 3 or \frac{2 L}{3}$

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