The x-z plane separates two media A and B of refractive indices `mu_(1) = 1.5` and `mu_(2) = 2`. A ray of light travels from A to B. Its directions in the two media are given by unit vectors `u_(1) = a hat(i)+b hat(j)` and `u_(2) = c hat(i) +a hat(j)`. Then

Explanation

tani = `a/b` so sini =`a/sqrt(a^(2)+b^(2))`
tanr = `c/d`, sinr =`c/sqrt(c^(2)+d^(2))`
`mu_(1)` sini = `mu_(2)`sinr, `(3/2) (a/sqrt(a^(2)+b^(2)) = 2(c/sqrt(c^(2) + d^(2)))`
But as `ahati` + `bhatj` and `chati` + `dhatj` are unit vectors so
`sqrt(a^(2)+b^(2)) = sqrt(c^(2) + d^(2))`=1 , Hence `3/2`a=2c, so `a/c = 4/3`