KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • 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

    Correct Answer: A

    Solution :

    \[i+r=90{}^\circ ,\]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       \[x=\frac{{{y}^{2}}}{2}=\frac{{{1}^{2}}}{2}=\frac{1}{2}\]

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