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A ray of light is incident from air on a surface of medium at an angle of $60^{\circ}$. The angle of refraction in the medium is $ 30^{\circ}$ what will be the velocity of light in the medium.

$(a)\;2.62 \times 10^{8}\;m/s \\ (b)\;1.26 \times 10^8\;m/s \\ (c)\;4.21 \times 10 ^8\;m/s \\ (d)\;1.73 \times 10^8\;m/s$

1 Answer

$\mu= \large\frac{Velocity \;of\;light\;in\;air}{Velocity\;of\;light\;in\;medium}$
$\qquad= \large\frac{ \sin i}{\sin r}$
$\large\frac{c}{v}= \frac{\sin 60}{\sin 30}$
$v= \large\frac{c \times\sin 30}{\sin 60}$
$\quad= \large\frac{3 \times 10^8 \times \Large\frac{1}{2}}{\Large\frac{\sqrt 3}{2}}$
$\quad= \large\frac{3 \times 10^8}{\sqrt 3}$
$\quad=1.73 \times 10^8 m/s$
Hence D is the correct answer.
answered Jan 16, 2014 by meena.p

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