Question

If the refractive index of medium $b$ with respect to medium $a$ and that of medium $c$ with respect to medium $b$ are given as $n_{ba}$ and $n_{cb}$ respectively, then the refractive index of a medium $c$ with respect to a medium $a$ can be found by using the relation
$n_{ca}=n_{ba}\times ........$

• A. $n_{cb}$
• B. $n_{ac}$
• C. $n_{ca}$
• D. $n_{ba}$

Answer 1

The correct option is A $n_{cb}$

The refractive index of medium $c$ with respect to $a$ is denoted as $n_{ca}$.

As per the definition, $n_{ca}=\frac{n_a}{n_c}$, where $n_c$ is the absolute refractive index of medium $c$ and $n_a$ is the absolute refractive index of medium $a$.

Now, $n_{ca}=\frac{n_a}{n_c}=\frac{n_a}{n_b}\times \frac{n_b}{n_c}$

$\frac{n_a}{n_b}=n_{ba}$ and $\frac{n_b}{n_c}=n_{cb}$

Thus we get,

$n_{ba}\times n_{cb}=n_{ca}$

So the answer is $n_{cb}$.