Question

Refractive index of diamond with respect to glass is 1.6 and the absolute refractive index of glass is 1.5. Find out the absolute refractive index of diamonds.
(A). 1.06
(B). 0.93
(C). 2.4
(D). 0.75

Answer 1

Hint – The absolute refractive index of glass can be obtained directly by using the formula, ${\mu _{dg}} = \dfrac{{{\mu _d}}}{{{\mu _g}}}$, here ${\mu _{dg}}$ is the refractive index of diamond with respect to glass, ${\mu _d},{\mu _g}$ are the absolute refractive index of diamond and glass.
Formula used - ${\mu _{dg}} = \dfrac{{{\mu _d}}}{{{\mu _g}}}$.

Complete step-by-step solution -
Given in the question that the refractive index of diamond with respect to glass is ${\mu _{dg}} = 1.6$
Also, the absolute refractive index of glass is ${\mu _g} = 1.5$
Now, let us first see what is a refractive index, so the refractive index is the ratio of the velocity of light in a vacuum to its velocity in a specified medium.
In optics, the refractive index of a material is a dimensionless number that is used to describe how fast light travels through the material.
Now, we know that the refractive index of diamond with respect to glass is related with the absolute refractive index of diamond and glass as-
${\mu _{dg}} = \dfrac{{{\mu _d}}}{{{\mu _g}}}$
Here, ${\mu _{dg}}$ is the refractive index of diamond with respect to glass and ${\mu _d},{\mu _g}$ are the absolute refractive index of diamond and glass.
So, we know, ${\mu _{dg}} = 1.6$ , ${\mu _g} = 1.5$ , putting these in above formula, we get-
$1.6 = \dfrac{{{\mu _d}}}{{1.5}}$
So, the absolute refractive index of diamond will be-
$ \Rightarrow {\mu _d} = 1.6 \times 1.5 = 2.4$
Hence, the correct option is C.

Note – Whenever such types of questions appear, then don’t get confused between the terms absolute refractive index and refractive index with respect to some other object, both these terms are different. Also, before solving, write down the things given in the question. And then as mentioned in the solution, using the formula for the refractive index of diamond with respect to glass, we have found the value of the absolute refractive index of a diamond.