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

Answer

B

Explanation

(b) We know that,
`1/mu=(sini)/(sinr')`
But `r+r'=90^(@)or r'=90^(@)-r`
`sinr'=sin(90^(@)-r')
=cosr
or sinr'=cosi
`therefore `1/mu=(sini)/(cosi)or1/mu=tani`
or `sini_(C)=tani=tanr`
The critical angle for pair of media is,
`i_(C)=sin^(-1)(tan(r))`