The reflecting surface is represented by the equation $2 x = y^{2}$ as shown in figure. A ray travelling horizontal becomes vertical after reflection. The co-ordinates of the point incidence can be

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$(1, 1 / 2)$

$(1 / 2, 1 / 2)$

$(1 / 2, 1)$

$(1 / 2, - 1)$

answer is A, D.

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Detailed Solution

At the point if incidence slope should be $\pm 1$

$y^{2} = 2 x y = \sqrt{2 x} \frac{d y}{d x} = \sqrt{2} . \frac{1}{2 \sqrt{x}} = \frac{1}{\sqrt{2 x}} = 1 \sqrt{2 x} = 1 2 x = 1 x = \frac{1}{2} \Rightarrow y = \pm 1 (\frac{1}{2}, \pm 1)$

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