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STD 12 - 9. Ray optics abd optical instruments — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 12 - 9. Ray optics abd optical instruments4 Marks
Question
$A$ reflecting surface is represented by the equation $Y = \frac{{2L}}{\pi }\,\sin \left( {\frac{{\pi \,x}}{L}} \right)$ , $0 \leq x \leq L$. A ray travelling horizontally becomes vertical after reflection. The coordinates of the point $(s)$ where this ray is incident is ?
✓

Answer

As the Incident ray is horizontal $0$ deg, and reacted ray is vertical $90$ deg.

So the slope at point of reaction should be $90-0 / 2=45^{\circ}$

The derivative of equation of mirror surface, we get

$\frac{d y}{d x}=2 \cos \left(\frac{\pi x}{L}\right)=\tan \left(45^{\circ}\right)=1$

so, $x=\frac{L}{3}$

and using equation of mirror surface,

$y=\frac{\sqrt{3} L}{\pi}$

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