A ray of light passes from vacuum into a medium of refractive index n . If the angle of incidence is twice the angle of refraction , then the relation between the angle of incidence and the refractive index is

Options

A. `n = 2 sin ((i)/(2))`
B. `n = 2 cos ((i)/(2))`
C. ` n = 2 tan ((i)/(2))`
D. `n = (1)/(2) [ cos ((i)/(2))]`

Answer

B

Explanation

`n = (sin i)/(sin r)`
It is given that `i=2r or r= (i)/(2)`
`therefore n = (sin i)/(sin ((i)/(2))) = (2 sin ((i)/(2)) cos ((i)/(2)))/(sin ((i)/(2))) = 2 cos ((i)/(2))`
`therefore n = 2 cos ((i)/(2))`