Question

The speed of light in diamond is 1,24,000 km/s. Find the refractive index of diamond if the speed of the light in air is 3,00,000 km/s.

Answer 1

Hint
The refractive index of a medium is given by the ratio of speed of light in vacuum to the speed of light in that particular medium. Substitute the speed of light in vacuum or air and in diamond in the formula. Simplify and calculate the refractive index of diamond.

Complete step by step answer
Light changes its speed when it travels from 1 medium to another medium. When it travels from denser medium to rarer medium, it bends away from the normal and when it travels from rarer medium to denser medium it moves towards the normal. the speed of light in any medium is given by Snell’s law and it is further manipulated to get the refractive index of a medium which is given by:
$ \operatorname Refractive\,index\,of\,a\,medium = \dfrac{{speed\,of\,light\,in\,vacuum}}{{speed\,of\,light\,in\,medium}} $
Refractive index of diamond = $ \operatorname Refractive\,index\,of\,a\,diamond = \dfrac{{3000000}}{{124000}} $
Therefore, the refractive index of diamond is: 2.41

Note
Refractive index depends on the nature of the media of incidence and refraction, colour of light or wavelength of light and temperature of the media. The minimum value of the refractive index is 1. For air it is very close to 1 that is 1.003 approximately.