If { }_{i} mu_{j} represents the refractive i | vedclass

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Question

(D) The refractive index of medium $j$ with respect to medium $i$ is defined as ${ }_{i} \mu_{j} = \frac{\mu_j}{\mu_i}$,where $\mu$ represents the abs

Vedclass · Accepted Answer

${ }_4 \mu_1$

Vedclass · Answer

(D) The refractive index of medium $j$ with respect to medium $i$ is defined as ${ }_{i} \mu_{j} = \frac{\mu_j}{\mu_i}$,where $\mu$ represents the absolute refractive index of the medium.Given the expression: ${ }_2 \mu_1 	imes { }_3 \mu_2 	imes { }_4 \mu_3$.Substituting the definition of refractive index:$= \frac{\mu_1}{\mu_2} 	imes \frac{\mu_2}{\mu_3} 	imes \frac{\mu_3}{\mu_4}$.Canceling the common terms in the numerator and denominator:$= \frac{\mu_1}{\mu_4}$.By definition,$\frac{\mu_1}{\mu_4} = { }_4 \mu_1$.However,looking at the options,we note that ${ }_4 \mu_1 = \frac{1}{{ }_1 \mu_4}$. Since the question asks for the equivalent product,and ${ }_4 \mu_1$ is the result,we check the provided options. Note that ${ }_4 \mu_1$ is equivalent to $\frac{1}{{ }_1 \mu_4}$. Given the structure of the options,there might be a typo in the question's options provided. Based on the derivation,the result is ${ }_4 \mu_1$.

If ${ }_{i} \mu_{j}$ represents the refractive index when a ray goes from medium $i$ to medium $j$,then the product ${ }_2 \mu_1 \times { }_3 \mu_2 \times { }_4 \mu_3$ is equal to:

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