A reflecting surface is represented by the equation
$y = \frac{2 L}{π} \sin (\frac{πx}{L}), 0 \leq x \leq L$
A ray travelling horizontally becomes vertical after reflection. The co-ordinate of the points where this ray is incident is

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$(\frac{L}{4}, \frac{\sqrt{2} L}{π})$

$(\frac{3 L}{4}, \frac{\sqrt{2} L}{π})$

$(\frac{2 L}{3}, \frac{\sqrt{3} L}{π})$

$(\frac{L}{3}, \frac{\sqrt{3} L}{π})$

answer is B, D.

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Detailed Solution

The slope of curve at such a point will be $\pm 1$
$∴ \frac{dy}{dx} = 2 \cos (\frac{πx}{L}) = \pm 1 \Rightarrow x = \frac{L}{3} or \frac{2 L}{3}$

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