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

`._(1)^(2)mu=(sin90^(@))/(sinC)=(1)/(sinC)` [For critical angle]
`:.C=sin^(-1)=((1)/(._(2)^(1)mu))` (i)
Applying Snell's law at P, we get
`._(2)^(1)mu=(sinr^('))/(sini)(sin(90-r))/(sinr) [:' i=r,r^(')+r=90^(@)]`
`:. ._(2)^(1)mu=(cosr)/(sinr)` (ii)
From (i) and (ii), `C=sin^(-1)(tanr)`