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 ?

Explanation

From Snell's law, we have
`(sin i)/(sin r)=mu_(g)/mu_(D)` or `mu=mu_(D)/mu_(g)` ...(i)
`=(sin r)/(sin i)`
According to the given problem,
`i+r+90^(@)=180^(@)`
or, `r=90^(@)-i`
Substituting the above value of 'r' in equation (i), we get
`mu=(sin(90^(@)-i))/(sin i)` or, `mu=cot i` ...(ii)
By definition `C=sin^(-1) (1/mu)`
or, `C=sin^(-1) (1/(cot i))` (using equation (ii))
or, `C=sin^(-1) (tan i)`