Question

Refractive index of glass with respect to air is 3÷2 what would be the value of refractive index of air with respect to glass?

Answer 1

Given :

▪ Refractive index of glass wrt air = 3/2

To Find :

▪ Reftactive index of air wrt glass.

Concept :

↗ Refractive index of medium is defined as the factor by which speed of light reduces as compated to the speed of light in vacuum.

$\bigstar\:\underline{\boxed{\bf{\red{n=\dfrac{c}{v}=\dfrac{speed\:of\:light\:in\:vacuum}{speed\:of\:light\:in\:medium}}}}}$

↗ More (less) refractive index implies less (more) speed of light in that medium, which therefore is called denser (rarer) medium.

↗ Refractive index of medium A wrt medium B is given by

$\bigstar\:\underline{\boxed{\bf{\blue{n_{AB}=\dfrac{n_A}{n_B}}}}}$

Calculation :

$\dashrightarrow\sf\:n_{ag}=\dfrac{n_a}{n_g}\\ \\ \dashrightarrow\sf\:n_{ag}=\dfrac{1}{n_{ga}}\\ \\ \dashrightarrow\underline{\boxed{\bf{\green{n_{ag}=\dfrac{2}{3}}}}}\:\orange{\bigstar}$

⚠ Extra Dose :

• Refractive index of a medium is an unitless as well as dimensionless quantity.

Answer 2

Given ,

Refractive index of glass with respect to air = 3/2

$\implies \bf{n_{ga}=\dfrac{n_g}{n_a}=\dfrac{3}{2}...(1)}$

We need to find the value of Refractive index of air with respect to glass.

We know that ,

Refractive index of A with respect to B is given by ,

$\implies \bf{n_{AB}=\dfrac{n_A}{n_B}}$

Now Refractive index of air with respect to glass is given by ,

$\implies \bf{n_{ag}=\dfrac{n_a}{n_g}}\\\\\implies \bf{n_{ag}=\dfrac{1}{n_g/n_a}}\\\\\implies \bf{n_{ag}=\dfrac{1}{3/2}\;[\;From\;(1)\;]}\\\\\implies \bf{\red{n_{ag}=\dfrac{2}{3} }}$

So refractive index of air with respect to glass is 2/3 .