A ray of light from a denser medium strikes a rarer medium at an angle of incidence i. if the reflected and the refracted rays are mutually perpendicular to each other, what is the value of the critical angle ?

Options

A. `sin^(-1) (cot i)`
B. `cos^(-1) (tan i)`
C. `sin^(-1) (tan i)`
D. `tan^(-1) (sin i)`

Answer

A

Explanation

`90^@ - i + 90^@ - r = 90`
`-(i+r) = 90 - 180^@`
`u = (sin i)/(sin r)`
`mu = (sin i)/(sin (90 - i))`
`mu = (sin i)/(cos i) = tan i`
`sin C = 1/mu`
`sin C = 1/(mu)`
`sin C = 1/("tan i")`
`c = sin^(-1) (cot i)`