A ray of light travels from air to glass . It is found that the angle of refraction is half the angle of incidence . Then the angle of refraction is given by

Options

A. `r= cos^(-1)""(n/2)`
B. `r=sin^(-1)(n/2)`
C. `r=tan^(-1)""(n/2) `
D. `r=cos^(-1)""(2/n)`

Answer

A

Explanation

`n=( sin i)/(sin r)=(sin 2r)/(sin r)=(2 isn r cos r )/( sin r)=2 cos r`
`:. cos r =(n)/2 :. r=cos^(-1)""(n/2)`