Two thin slabs of refractive indices `mu_(1)` and `mu_(2)` are placed parallel to each other in the x-z plane. If the direction of propagation of a ray in the two media are along the vectors `vec(r)_(1) = a hati +b hatj` and `vec(r)_(2) = c hati +d hatj` then we have:

Options

A. `mu_(1)a = mu_(2)c`
B. `mu_(1)(a^(2) + b^(2)) = mu_(2)(c^(2) + d^(2))`
C. `mu_(1)a//sqrt(a^(2) + b^(2)) = mu_(2)a//sqrt(c^(2) + d^(2))`
D. None of these

Answer

A

Explanation

For parallel composite slab
`mu"sin"theta = "constant"`
`(mu_(1)xxa)/(sqrt(a^(2) + b^(2))) = (mu_(2) xx c)/(sqrt(c^(2) + d^(2)))`
`because |hatr_(1)| =|hatr_(2)| = 1 therefore (sqrt(a^(2) + b^(2))= sqrt(c^(2) + d^(2)) = 1)`
`therefore mu_(1)a = mu_(2)c`