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

D

Explanation

Incident angle from given plane
`theta_(1) = cos^(-1) ((vecA.veck)/(A))`
= `cos^(-1) ((-10)/(20)) = cos^(-1) ((-1)/(2)) = ((pi)/(3))`
Now by snell's law `n_(1) "sin"theta_(1) = n_(2) "sin"theta_(2)`
`"sin"theta_(2) = ((n_(1)/(n_(2))) "sin"theta_(1) = ((sqrt(2))/(sqrt(3)))((sqrt(3))/(2)) = (1)/(sqrt(2))`
`implies theta_(2) = 45^(@)`