# JEE Class main Answered

**Solve**

Asked by sarveshvibrantacademy | 16 May, 2019, 10:53: AM

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 μ

_{x}= 1+x^{2}. Let the ray makes angle of incidence θ_{x}at Q in the medium.If the given medium is in the form of rectangular slab, we have, 1×sinθ = μ

_{x}× sinθ_{x}or sinθ_{x}= sinθ / μ_{x}..................(1)hence we have, tanθ

_{x}= (dy/dx) = ..........................(2)if the incident light ray is nearly parallel to y-axis, then agle of incidence θ = π/2 .

At x = 1, refractive index μ

_{x}= 1+x^{2}= 1+1^{2}= 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/√3Hence 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 Thiyagarajan K | 16 May, 2019, 09:27: PM

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