• # question_answer The reflecting surface is represented by the equation $2x={{y}^{2}}$ as shown in the figure. A ray travelling horizontal becomes vertical after reflection. The co-ordinates of the point of incidence are: A) (1/2, 1) B) (1, 1/2)           C) (1/2, 1/2) D) none

 $i+r=90{}^\circ ,$and$\angle i=\angle r$ $\therefore$      $i=45{}^\circ$ Also      $i+\theta =90{}^\circ$ $\therefore$      $\theta =90{}^\circ -i=90{}^\circ -45{}^\circ =45{}^\circ$ Given                ${{y}^{2}}=2x$ Or    $2y\frac{dy}{dx}=2$ $\therefore$      $\frac{dy}{dx}=\frac{1}{y}$ Or            $tan45{}^\circ =\frac{1}{y}$ $\therefore$      $y=1$ Now       $x=\frac{{{y}^{2}}}{2}=\frac{{{1}^{2}}}{2}=\frac{1}{2}$