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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 $a$ .

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\frac{9}{8}

\frac{8}{9}

\frac{2}{7}

None of the above

answer is A.

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Detailed Solution

Refractive index of medium c with respect to medium

a

n_{a}^{c} = \frac{9}{8}

Given data:
Refractive index of the medium

‘ a ’

w.r.t

‘ b ’

\Rightarrow

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,

\Rightarrow

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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