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. `tan^(-1)("sin"r)`
C. `sin^(-1)("tan"r')`
D. `tan^(-1)("sin"r')`

Answer

A

Explanation

As given : r + r' = `90^(@)`
`u_(2)"sin"r = u_(1)"sin"r`
`implies u_(2) "sin"r = u_(1)"sin"(90-r)`
`u_(2)"sin"C = u_(1)"sin"90^(@)`
`(mu_(1))/(mu_(2)) = "tan"r , "sin"C = (mu_(1))/(mu_(2))`
(C : "Critical angle" )
`therefore "sin"C = "tan"r, C = sin^(-1)("tan"r)`