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

Answer

C

Explanation

`._Dmu_(R)=(sin i)/(sin r^('))implies._(R)mu_(D)=(sin r^('))/(sin i)=(1)/(sin C)`
`=sin C=(sin i)/(sin (90-r))=(sin i)/(cosr)=(sin i)/(cosi)` (as `/_i=/_r`)
`implies sin C = tan i implies C=sin ^(-1)(tan i)`