The XY plane is the boundary between two tranparednt media. Medium 1 with `z ge 0` has a refraxtive index of `sqrt2` and medium 2 with `z le 0` has a refractive index of `sqrt3`. A ray of light in medium 1 given by the vector `6sqrt(3)hat(i)+8sqrt(3)hat(j)-10hatk` is incident on teh plane of separation. Find the unit vector in the direction of teh refracted ray in medium 2.

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^(@)`