A ray of light passes from glass having a refractive index of `1.6,` to air. The angle of incidence for which the angle of refraction is twice the angle of incidence is

Options

A. `sin^(-1)((4)/(5))`
B. `sin^(-1)((3)/(5))`
C. `sin^(-1)((5)/(8))`
D. `sin^(-1)((2)/(5))`

Answer

B

Explanation

`._(g)mu_(a)=(sin)/(sin r)implies (1)/(._(a)mu_(g))=(sin i)/(sn 2i)`
`(1)/(16)=(sin i)/(2 sin i cos i )` or `(1)/(2 cos i)=(10)/(16)=(5)/(8)`
or `(1)/(cosi)=(5)/(4)` or `cos i=(4)/(5)`
Now, `sin i=sqrt(1-cos^(2))i`
or `sin r=sqrt(1-(16)/(265))=sqrt((9)/(25))=(3)/(5)`
or `i=sin ^(-1).((3)/(5))`
`impliessin C=(10t_(1))/(t_(2))impliesC sin ^(-1)((10t_(1))/(t_(2)))`