A ray of light is incident on a medium at an angle i. It is found that the reflected ray is at right angles to the refracted ray . The refractive index of the medium is given by

Options

A. `mu=(1)/(tantheta)`
B. `mu=tan^(2)theta`
C. `mu=sintheta`
D. `mu=tantheta`

Answer

D

Explanation

Angle of incidence `/_AON=theta`.
`bar(OB)` is the reflected ray and `bar(OC)`
is the reflected ray. It is given that
`/_BOC=90^(@)`
`:.` From the diagram
`theta+/_BOC+r=180^(@)`
or `theta+90^(@)+r=180^(@)`
or `r=90^(@)-theta`
`:.` Refractive index,
`mu=(sini)/(sinr)=(sintheta)/(sin(90^(@)-theta))=(sintheta)/(costheta)=tantheta`