If a ray of light in a denser medium strikes a rarer medium at an angle of incidence `i`, the angle of reflection and refraction are respectively r and r', if the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of media is

Options

A. `sin^(-1)(tanr')`
B. `sin^(-1)(tanr)`
C. `tan^(-1)(sini)`
D. `cot^(-1)(tani)`

Answer

A

Explanation

`r+r.=90^(@)` (given)
`therefore i+r.=90^(@)impliestani=cotr.`

From Brewster.s law `tani=mu=(1)/(sinC)`
`sinC=(1)/(tani)=(1)/(cotr.)=tanr.`
`impliesC=sin^(-1)(tanr.)`