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Asked by sarveshvibrantacademy
16th May 2019,
10:53 AM
Answered by Expert
Answer:
As shown in figure let a light ray enters at P and makes angle of incidence θ with y-axis.
Let the refractive index of the medium changes as μx = 1+x2 . Let the ray makes angle of incidence θx at Q in the medium.
If the given medium is in the form of rectangular slab, we have, 1×sinθ = μx × sinθx or sinθx = sinθ / μx ..................(1)
hence we have, tanθx = (dy/dx) = 
..........................(2)
..........................(2)if the incident light ray is nearly parallel to y-axis, then agle of incidence θ = π/2 .
At x = 1, refractive index μx = 1+x2 = 1+12 = 2 .
By substituting values in eqn.(2), we get (dy/dx) at x=1 for the light ray entering almost parallel to y-axis as (dy/dx)x=1 = 1/√3
Hence unit vector of the light ray at the point Q = (√3/2) i + (1/2) j , where i and j are unit vectors along x and y directions
Answered by Expert
16th May 2019,
9:27 PM
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