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       \[x=\frac{{{y}^{2}}}{2}=\frac{{{1}^{2}}}{2}=\frac{1}{2}\]