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. `60^(@)`
B. `75^(@)`
C. `30^(@)`
D. `45^(@)`

Answer

4

Explanation

Normal to the plane is z-axis
`costheta_(1)=(A_(z))/(A)=(10)/(20)=(1)/(2),theta_(1)=60`
`mu_(1)Sintheta_(1) rArr mu_(2) sintheta_(2) rArr sqrt(2)xx(sqrt(3))/(2)=sqrt(3)sintheta_(2) rArr theta_(2)=45^(@)`