At what value of the angle of incident `theta_(1)` is a shaft of light reflected from the surface of water perpendicular to the refracted shaft?

Explanation

Let `PQ` be the surface of water and `n` be the `R.I` of water. Let `AO` I sthe shalf o flight with incident angle `theta_(1)` and `OB` and `OC` are the reflected and refacted light rays at angles `theta_(1)` and `theta_(2)` respectively (Fig.) From the figure `theta_(2) = (pi)/(2)-theta_(1)`
From the law of refraction at the intenface `PQ`
`n = (sin theta_(1))/(sin theta_(2)) = (sin theta)/(sin((pi)/(2)-theta_(1)))`
or, `n = (sin theta_(1))/(cos theta_(1)) = tan theta_(1)`
Hence `theta_(1) = tan^(-1)n`