Question

The unit of refractive index is:
(a) m/s
(b) no units
(c) kg/$m^3$
(d) N

Answer 1

- Hint: Refractive index is the ratio of speed of radiation in vacuum to the speed of radiation in the given medium.

Complete step-by-step solution -

In our everyday life, we come across objects that are often represented in units. For instance, time is measured in seconds, minutes and hours, in the same way, speed of a vehicle is measured in kilometres per hour.
In optics, when there is a need to know how speed the light travels through a material, refractive index is used. Refractive index, also called the index of refraction, was first used and invented by Thomas Young in 1807. Newton called the refractive index as the proportion of the sine of incidence and sine of refraction and expressed it as the ratio of two numbers. It is denoted by the letter ‘n’.
Hence, we can write a refractive index as the ratio of speed of light in vacuum to the ratio of speed of light in a given medium. A few examples of the medium are glass, air, diamond, and water.
\[\text{n}=\dfrac{\text{c}}{\text{v}}\],
Here, n is a refractive index, c is the speed of light in vacuum and v is the speed of light in the medium.
Let us consider an example to calculate the refractive index and derive the unit of it. Consider a medium in which the speed of light is 1.2 x 108 metre per second (m/s). In this case, we can derive the refractive index as follows:
First, consider the formula of refractive index,
\[\text{n}=\dfrac{\text{c}}{\text{v}}\],
The value of v is given as 1.2 x 108 metre per second (m/s) and the speed of light in vacuum is always 3 x 108 metre per second (m/s). hence, substituting values of c and v in the formula, we get,
\[\text{n}=\dfrac{3\text{x1}{{\text{0}}^{8}}\text{m/s}}{1.2\text{x1}{{\text{0}}^{8}}\text{m/s}}=\dfrac{3}{1.2}=2.5\],
Hence the value of refractive index, n is 2.5. we can observe that the units of speed is m/s and is cancelled out in both numerator and denominator. Hence, the refractive index has no dimension and hence no units.

Note: Refractive index has no unit. The refractive index of air is 1.0003, water has a refractive index of 1.333. Diamond has the highest refractive index of 2.417.