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A reflecting surface is represented by t...

A reflecting surface is represented by the equation
`y = (2L)/(pi) sin ((pi x)/(L))`, where `0 le x le L`. A ray of light travelling horizontally becomes vertical after reflection with the surface. The co-ordinates of the point where this ray is incident is.

A

`((L)/(4),(sqrt(2)L)/(pi))`

B

`((L)/(3),(sqrt(3)L)/(pi))`

C

`((3L)/(4),(sqrt(2)L)/(pi))`

D

`((2L)/(3),(sqrt(3)L)/(pi))`

Text Solution

Verified by Experts

The correct Answer is:
B,D

`(dy)/(dt) =tan45^(@)`
`y=(2L)/(pi)sin((pix)/(L)) rArr (dy)/(dx)=(2L)/(pi) cos((pix)/(L))xx(pi)/(L)`
`(1)/(2)=(cospi)/(L)x rArr (cos2pi)/(3),(cospi)/(3)=(cospi)/(L)x`
`(2pi)/(3),(pi)/(3)=(pi)/(L)x rArr x=(L)/(3),(2L)/(3)`
`y_(1)=(2L)/(pi)sin((pi)/(L)xx(L)/(3)) rArr y_(1)=(2L)/(pi)sin(pi)/(3)`
`y_(1)=(sqrt(3)L)/(pi) rArr y_(2)=(2L)/(pi)sin((pi)/(L)xx(2L)/(3)) rArr y=(sqrt(3)L)/(pi)`
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