A ray of light from a denser medium strike a rarer medium at an angle of incidence I (see Fig). The reflected and refracted rays make as angle of 90degrees with each other. The angles of reflection and refraction are r and `r` The critical angle is

Options

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

Answer

A

Explanation

`C=Sin^-1((1)/(_2^1mu))` .....(i)
Applying Snell's law at P, we get `_2^1mu=(sinr`)/(sini)=sin(90-r)/(9sinr)` `[:' i=r^.,r^`+r=90degree]`
:' ` _2^1mu=(cosr)/(sinr)` ….(ii)
From (i) and (ii)
`C=sin^-1 (tanr)`