Question

If the refractive index of a certain material X with respect to air is 1.5, what is the refractive index of air with respect to the material X?​

Answer 1

Answer:

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Answer 2

Given is the refractive index of material X with respect to air as $=1.5$

We need to find the refractive index of air with respect to material X.

As we know:-

Refractive Index of X with respect to air(a) ($X^{n_{a} }$)= $\frac{Refractive index of material X}{Refractive Index of air a} =\frac{n_{X} }{n_{a} }$

Therefore, x$n_{a}=\frac{n_{X} }{n_{a} }=1.5$

Similarly, the refractive index of air with respect to material X is a $n_{x}=\frac{n_{a} }{n_{x} }$

Let us take  $\frac{1}{a^{n_{x} } } } = \frac{n_{X} }{n_{a} }=X^{n_{a} }$

That gives us   $\frac{1}{a^{n_{X} } } = X^{n_{a} }$

⇒$a^{n_{X} } =\frac{1}{X^{n_{a} } } =\frac{1}{1.5} =\frac{10}{15}=\frac{2}{3}=0.66$

Hence, the refractive index of air with respect to material X is $0.66$