State the law of refraction of light that defines the refractive index of a medium with respect to the other. Express it mathematically. How is refractive index of any medium ‘A’ with respect to a medium ‘B’ related to the speed of propagation of light in two media A and B? State the name of this constant when one medium is vacuum or air. The refractive indices of glass and water with respect to vacuum are 3/2 and 4/3 respectively. If the speed of light in glass is 2 x 108 m/s, find the speed of light in (i) vacuum, (ii) water.
Snell’s law: The ratio of sine of angle of incidence (i.e. sin i) to the sine of angle of refraction (i.e. sin r) is always constant for the light of given colour and for the given pair of media.
Mathematically,
sin i/sin r = constant = n21
The constant 'n21' is called refractive index of the second medium with respect to the first medium.
Refractive index of medium 'A' with respect to medium 'B' is represented by nAB. It is given by
nAB = Speed of light in medium 'B'/Speed of light in medium 'A'
= vB/VA
If one medium is vacuum or air, then the refractive index of the second medium with respect to vacuum or air is called absolute refractive index of the medium, nm.
Thus,
nm = Speed of light in air or vacuum/Speed of light in medium = c/v