Question

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

Answer 1

Hint The refractive index is the ratio of the velocity of light in a vacuum to its velocity in the medium of which the refractive index has to be calculated. The refractive index of a medium $A$ with respect to the medium $B$ is the ratio of the velocity of light in the medium $B$ to the velocity of light in the medium$A$.
Formula used
${\mu _{dg}} = \dfrac{{{\mu _d}}}{{{\mu _g}}}$
Where ${\mu _{dg}}$the refractive index of a diamond as compared to glass. ${\mu _g}$,${\mu _d}$ are the absolute refractive index of glass and diamond respectively.

Complete Step-by-step solution
It is given in the question that
The refractive index of a diamond as compared to glass is $1.6$.
The absolute refractive index of a glass is $1.5$.
We know that,
The refractive index of a medium is a dimensionless quantity that signifies how fast light travels in a given medium.
And,
${\mu _{dg}} = \dfrac{{{\mu _d}}}{{{\mu _g}}}$
Where ${\mu _{dg}}$ the refractive index of a diamond as compared to glass. ${\mu _g}$,${\mu _d}$ are the absolute refractive index of glass and diamond respectively.
From this formula and the data given in the question,
${\mu _{dg}} = 1.6$ and ${\mu _g} = 1.5$
So we can say that
$1.6 = \dfrac{{{\mu _d}}}{{1.5}}$
${\mu _d} = 1.6 \times 1.5$
${\mu _d} = 2.4$
The absolute refractive index of diamond is found to be $2.4$.

Therefore the correct answer to our question is (C) $2.4$.

Note
Whenever such types of questions appear, then do not 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 any question develop a habit of writing down the data given in the question and the formulas which can be useful to solve the question then start solving the question.