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. $2.4$
B. $1.6$
C. $1.06$
D. None of the above

Answer 1

When a light ray travelling in medium (1) enters medium (2) then the refractive index of medium (2) with respect to medium (1) is defined to be a relative refractive index. It is equal to the ratio of the refractive index of medium (2) to the refractive index of medium (1).

Complete step by step answer:
We all know that the speed of light is different in different mediums. When a light ray passes from one medium to another, the speed of light changes. The medium in which the speed of light is faster is called the rarer medium and the medium in which the speed of light is slower is called denser medium. Due to the change in speed, the light ray appears to bend at the interface of the two mediums. This bending of light is called refraction.

To understand the speed of light in a medium, we have something known as refractive index (also called absolute refractive index). Refractive index ($\mu$) of a medium is that characteristic which decides the speed of light. Refractive index of a medium is the ratio of the speed of light in vacuum (c) to the speed of light (v) in the given medium i.e. $\mu =\dfrac{c}{v}$.

To compare the refractive indices of different mediums we have a relative refractive index. When a light ray travelling in medium (1) enters medium (2) than the refractive index of medium (2) with respect to medium (1) is defined to relative refractive index and is written as ${}_{1}{{\mu }_{2}}$.
${}_{1}{{\mu }_{2}}=\dfrac{{{\mu }_{2}}}{{{\mu }_{1}}}$ ……….(1)

Let the absolute refractive index of glass be ${{\mu }_{1}}$ and the absolute refractive index of diamond be ${{\mu }_{2}}$. Then the refractive index of diamond with respect to glass is ${}_{1}{{\mu }_{2}}=\dfrac{{{\mu }_{2}}}{{{\mu }_{1}}}$ ……….(1)
It is given that ${{\mu }_{1}}=1.5$ and ${}_{1}{{\mu }_{2}}=1.6$.
Substitute these values in (i).
$1.6=\dfrac{{{\mu }_{2}}}{1.5}$
$\Rightarrow {{\mu }_{2}}=1.5\times 1.6\\\ \therefore {{\mu }_{2}}=2.4$.
This means that the absolute refractive index of diamond is $2.4$.

Hence, the correct option is A.

Note: If ${}_{1}{{\mu }_{2}}$ is the relative refractive index of medium (2) w.r.t medium (1). Then ${}_{2}{{\mu }_{1}}$ is the relative refractive index of medium (1) w.r.t medium (2). Therefore,
${}_{2}{{\mu }_{1}}=\dfrac{{{\mu }_{1}}}{{{\mu }_{2}}}\\\ \Rightarrow {}_{2}{{\mu }_{1}}=\dfrac{\dfrac{c}{{{v}_{1}}}}{\dfrac{c}{{{v}_{2}}}}\\\ \Rightarrow {}_{2}{{\mu }_{1}}=\dfrac{{{v}_{2}}}{{{v}_{1}}}$ ……..(2)
Multiply the equations (1) and (2).
We get,
${}_{1}{{\mu }_{2}}.{}_{2}{{\mu}_{1}}=\dfrac{{{v}_{1}}}{{{v}_{2}}}.\dfrac{{{v}_{2}}}{{{v}_{1}}}\\\ \Rightarrow {}_{1}{{\mu }_{2}}.{}_{2}{{\mu}_{1}}=1$
$\therefore {}_{1}{{\mu }_{2}}=\dfrac{1}{{}_{2}{{\mu }_{1}}}$