First slide

Refraction of light

Question

The refractive index of medium of a rectangular slab varies as $μ = \sqrt{1 + γ}$ . The ray enter from air to slab at origin in the condition of grazing incidence. The trajectory of ray inside slab is

Moderate

A

Straight line
B

parabola
C

ellipse
D

circle

Solution

Here, $u \sin θ = K$

Or $\sqrt{1 + y} \sin θ = K$
For air $1 \times \sin 90^{0} = K$ (grazing incidence)
$∴ K = 1$
$\begin{array}{l} \sqrt{1 + y} \sin θ = 1 \\ ∴ \sin θ = \frac{1}{\sqrt{1 + y}} \\ \Rightarrow \tan θ = \frac{1}{\sqrt{1 + y - 1}} = \frac{1}{\sqrt{y}} \\ \Rightarrow \frac{d x}{d y} = \frac{1}{\sqrt{y}} \\ \Rightarrow_{0}^{x} d x =_{0}^{y} \frac{1}{\sqrt{y}} d y \\ \Rightarrow x = {[\frac{y^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1}]}_{0}^{y} \\ \Rightarrow x = {[2 \sqrt{y}]}_{0}^{y} \\ \Rightarrow x = 2 \sqrt{y} \\ \Rightarrow x^{2} = 4 y \end{array}$

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