A ray of light from a denser medium strikes a rarer medium at an angle of incidenc i. The reflected and refracted rays make an angle of `pi//2` with each other. If the angles of reflection and refraction are r and `r^(')` , then the criticall angle will be

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)`