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

Explanation

We know that, `(1)/(mu)=(sini)/(sinr')`
But `r+r'=90^(@)orr'=90^(@)-r`
`sinr'=sin(90^(@)-r')`
= cos r
or `sinr'=cosi`
`therefore (1)/(mu)=(sini)/(cosi)or(1)/(mu)=tani`
or `sini_(C)=tani=tanr`
The critical angle for pair of media is,
`i_(C)=sin^(-1)(tanr)`