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.

Options

A. `((L)/(4), (sqrt2L)/(pi))`
B. `((L)/(3), (sqrt3L)/(pi))`
C. `((3L)/(4), (sqrt2L)/(pi))`
D. `((2L)/(3), (sqrt3L)/(pi))`

Answer

B

Explanation

`((dy)/(dx))_("tangent") = 2 cos (pi x)/(L)`
and tan `(90 + 45^(@)) = ((dy)/(dx))_("normal")`
`rArr x = (L)/(3), y = (sqrt3L)/(pi)`