A light ray enters into a medium whose refractive index varies along x-axis as $y(x) = \mu_{circ} \sqrt {1+ 0.25 x}.$ Where $\mu_0=1$.The medium is bounded by the planes $x=0,x=1\;cm$ and $y=0$ . If the ray enters at an angle $\theta=30^{\circ}$ with horizontal . Then the trajectory of light ray is

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$(a)\;y=\sqrt x+3 \\ (b)\;y= 2[ \sqrt {x+3} -\sqrt 3] \\ (c)\;y=2 \sqrt {x+3} \\ (d)\;y=2\sqrt 3 $