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Q.

The refractive index of a medium $a$ with respect to medium $b$ is $\frac{2}{3}$ and the refractive index of medium $b$ with respect to medium $c$ is $\frac{3}{4}$ . Refractive index of medium $c$ with respect to medium $a$ is __________________________________________.

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a

\frac{9}{8}

b

$\frac{8}{7}$

c

\frac{2}{7}

d

\frac{8}{9}

answer is A.

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Detailed Solution

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Given data:
Refractive index of the medium a w.r.t b,

$n_{ab} = \frac{v_{b}}{v_{a}}$ $= \frac{2}{3}$
$\Rightarrow v_{a} = \frac{3}{2} v_{b}$
Refractive index of the medium b w.r.t medium c,

$\Rightarrow n_{bc} = \frac{v_{c}}{v_{b}}$ $= \frac{3}{4}$
$\Rightarrow v_{c} = \frac{4}{3} v_{b}$
Refractive index of medium c with respect to medium a,
$n_{a}^{c} = \frac{v_{a}}{v_{c}}$ $= \frac{\frac{3}{2} v_{b}}{\frac{4}{3} v_{b}}$
$= \frac{9}{8}$

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