A ray of light enters from a rarer to a denser medium. The angle of incidence is I . Then the reflected and refracted rays are mutually perpendicular to each other . The critical angle for the pair of media is

Options

A. `sin^(-1)(coti)`
B. `cos^(-1)(tani)`
C. `sin^(-1)(tani)`
D. `tan^(-1)(sini)`

Answer

A

Explanation

`90^(@)-i+90^(@)-r=90` degrees.
`thereforei+r=90^(@)`
`rArrmu=(sini)/(sinr)=(sini)/(sin(90^(@)-i))=tani`
`(sin90^(@))/(sinC)=murArrsinC=(1)/(tani)=coti`
`therefore`C, the critical angle `=sin^(-1)(coti)`.