Question

The speed of light in diamond is 125000 km/s. What is its refractive index?
(Speed of light in air = $3\times {{10}^{8\ }}\ \text{m/s}$ )

(A). $\dfrac{1}{2.4}$
(B). 2.4
(C). 1.2
(D). $\dfrac{1}{1.2}$

Answer 1

The refractive index of the material is the ratio of the speed of light in air and the speed of light in the material. It is the dimensionless quantity because it is the ratio of the same quantity.

Complete step-by-step answer :
Given:
The speed of the light in diamond is, v=125000 km/s
Speed of light in air is, c= $3\times {{10}^{8\ }}\ \text{m/s}$

The speed of the light in diamond is, v=125000 km/s
The speed of the light in diamond in SI system is, $v=12500\times 1000\ \text{m/s}$

The refractive index of diamond is given as:
$\Rightarrow R.I=\dfrac{c}{v}$
Where, c is the speed of light in air and v is the speed of light in diamond
$\begin{aligned} & \Rightarrow R.I.=\dfrac{3\times {{10}^{8}}\ \text{m/s}}{12500\times 1000\ \text{m/s}} \\\ & \Rightarrow R.I.=2.4 \end{aligned}$
So, option B is correct.

Note : The speed of light in air is given as, c= $3\times {{10}^{8\ }}\ \text{m/s}$
The speed of the light in diamond is, v = 125000 km/s
Both quantities represent the speed of light but in different units. If the unit conversion part is missed by you. You will end with the wrong answer.