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

Options

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

Answer

c.

Explanation

`mu=(sinr^('))/(sini)`
But `r^(')+r=90^(@)`
or `r^(')=90^(@)-r`
`r=90^(@)-r`
`:. mu=(cosi)/(sini)`
or `(1)/(sini_(c))=(1)/(tani)`
or `i_(c)=sin^(-1)(tani)`