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

Options

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

Answer

A, B

Explanation

Imagine the entire path of beam is reversed. Therefore, the wave incident at `/_r'` gets polarised on reflection. According to Brewster's law, Fig.
`mu = tan r' = tan (90^(@) - r) = cot r`
But `mu = (1)/(sin C) =cot r = (1)/(tan r)`
`:. sin C = tan r, C = sin^(-1)(tan r)`
As `r = i`
`:. C = sin^(-1)(tan r) = sin^(-1)(tan i)`