Let the x-z plane be the boundary between two transparent media. Medium 1 in `zge0` has a refractive index of `sqrt2` and medium 2 with `zlt0` has a refractive index of `sqrt3`. A ray of light in medium 1 given by the vector `vecA=6sqrt3hati+8sqrt3hatj-10hatk` is incident on the plane of separation. The angle of refraction in medium 2 is:

Options

A. `30^(@)`
B. `46^(@)`
C. `60^(@)`
D. `75^(@)`

Answer

B

Explanation

`X-Y` axis
`mu_(1) sintheta_(1)=mu_(2)sintheta_(2)`
`costheta_(1)=(10)/(sqrt((6sqrt3)+(8sqrt(3))^(2)+100))=(10)/(sqrt(400))=(10)/(20)`
`costheta_(1)=(1)/(2)`
`theta_(1)=60^(@)`
`sqrt2 sin60^(@)=sqrt3 sintheta_(2)`
`sqrt2xx(sqrt3)/(2)=sqrt3sintheta_(2)`
`sintheta_(2)=(1)/(sqrt2)`
`theta=45^(@)`