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# Find speed of light in medium 'a' if speed of light in medium 'b' is $\large\frac{c}{3}$ where $c=$ Speed of light in vaccum and light refracts from medium 'a' to medium 'b' making $45^{\circ}$ and $60^{\circ}$ respective with normal.

$(a)\;Va= \frac{\sqrt 2}{\sqrt 3}C \\ (b)\;Va= \frac{\sqrt 2}{3 \sqrt 3}C \\ (c)\;Va= \frac{3 \sqrt 2}{\sqrt 3}C \\ (d)\; Va=\sqrt {\frac{3}{2}}C$

By Snell's law
$\mu_a \sin \theta_a = \mu b \sin \theta_b$
$\large\frac{c}{V_a}$$\sin \theta_a=\large\frac{C}{Vp}$$ \sin \theta_b$
$\large\frac{C}{V_a} $$\sin 45^{\circ}=\large\frac{c}{c/3}$$\sin 60^{\circ}$
$Va= \large\frac{\sqrt 2}{3 \sqrt 3}$$C$
Hence b is the correct answer.