A ray of light is incident on a transparent glass slab of refractive index `sqrt3`. If the reflected and refracted rays are mutually perpendicular, what is the angle of incidence?

Explanation

Let the angle of incidence, angle of reflection, and angle of refraction be i , r and `r^(')`, respectively.
Now, as per the equation `(90^(@)-r)+(90^(@)-r^(')) = 90^(@)`
`r^(')`=`(90^(@) -i)` (because i=r, in case of reflection according to Snell's law, 1 sin i =`mu sinr^(')`)
or sin i= `mu sin r^(')`
or sin i =`mu sin(90^(@)-i) rArr tan i=mu`
or `i=tan^(-1) mu =tan^(-1)sqrt3=60^(@)`