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

Options

A. `a/c=4/3`
B. `a/c=3/4`
C. `b/d=4/3`
D. `b/d=3/4`

Answer

A

Explanation

As `ahat(i)+bhat(j)` and `chat(i)+dhat(j)` are unit vectors their x components represent `sin theta`
`1.5sin i=2sin r`
`a=xx1.5=2xxc`
`a/b=4/3`