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 direction in the two media are given by unit vectors `vec(u)_(1)=a hat(i) + b hat(j)` and `vec(u)_(2)= chat(i)+dhat(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

From Snell's law , 1.5 sin I = 2 sin r
`1.5 xx (a)/(sqrt(a^(2)+b^(2)))=2 xx (c)/(sqrt(c^(2)+ d^(2))) implies (a)/(c) = (4)/(3)`
`[because sqrt(a^(2)+b^(2) )= sqrt(c^(2)+d^(2)) = 1` ("unit vector" )]