Question

What is called the absolute refractive index of a medium? Obtain a general form of Snell’s law in terms of refractive indices of two media?

Answer 1

Hint: Refractive index of a medium is the degree of deviation produced when a ray of light travels from vacuum to other medium. Refractive index of any medium can be defined in terms of many factors. As refractive index is dimensionless figure and besides this, it is ratio of two quantities of similar dimensions hence related quantities are generally compared such as velocity, degree of rotation, density etc.

Complete step by step solution:
Relative Refractive Index: When a ray of light travelling from a medium exits that medium to enter another medium of different density, the ray shows a certain amount of deviation (based on density of medium) in its velocity. This change in velocity when compared in terms of ratio becomes the refractive index of that medium.
$\dfrac{{{n_1}}}{{{n_2}}} = \dfrac{{{v_2}}}{{{v_1}}}$
${n_1} = \,{\text{refractive}}\,{\text{index}}\,{\text{of}}\,{\text{incident}}\,{\text{medium}}$
${n_2} = \,{\text{refractive}}\,{\text{index}}\,{\text{of}}\,{\text{refracted}}\,{\text{medium}}$
${v_{2\,}}\, = \,{\text{velocity}}\,{\text{of}}\,{\text{light}}\,{\text{in}}\,{\text{refracted}}\,{\text{medium}}$
${v_1}\, = \,{\text{velocity}}\,{\text{of}}\,{\text{light}}\,{\text{in}}\,{\text{incident}}\,{\text{medium}}$
Absolute Refractive Index: In contrast to relative refractive index when a light travels from vacuum to another medium (not from any medium to other), at this point the ratio of change of its velocity becomes its absolute refractive index. i.eWhen light travels from vacuum to another medium it gives an absolute refractive index and when it travels from one medium to another it gives relative refractive index.
$n = \dfrac{c}{v}$
$n = \,{\text{refractive}}\,{\text{index}}\,{\text{of}}\,{\text{medium}}$
$c = {\text{velocity}}\,{\text{of}}\,{\text{light}}\,{\text{in}}\,{\text{vacuum}}$
$v = {\text{velocity}}\,{\text{of}}\,{\text{light}}\,{\text{in}}\,{\text{medium}}$
It can also be said that every absolute R.I. is a relative refractive index but every relative R.I. is not absolute R.I.
Refractive index is represented by Snell’s law. Snell’s law states the relation between angle of incidence and angle of refraction in terms of refractive index of medium. According to Snell’s law’
$n = \dfrac{{\sin i}}{{\sin r}}$
Where, $n = \,{\text{refractive}}\,{\text{index}}\,{\text{of}}\,{\text{medium}}$
              $i = \,{\text{angle}}\,{\text{of}}\,{\text{incidence}}$
               $r = \,{\text{angle}}\,{\text{of}}\,{\text{refraction}}$
Now applying wave theory of light to the Snell’s law equation, we can relate velocity of light with angle of incidence and refraction as,
$n = \dfrac{{\sin i}}{{\sin r}} = \dfrac{{{\text{velocity}}\,{\text{of}}\,{\text{light}}\,{\text{in}}\,{\text{vacuum}}}}{{{\text{velocity}}\,{\text{of}}\,{\text{light}}\,{\text{in}}\,{\text{medium}}}}$
The above equation is for the case when light passes from vacuum to medium, in case when light passes from medium 1 to medium 2, Snell’s law can be written as:
$\dfrac{{{n_2}}}{{{n_1}}} = \dfrac{{\sin i}}{{\sin r}} = \dfrac{{{v_i}}}{{{v_r}}}$
${n_1} = \,{\text{refractive}}\,{\text{index}}\,{\text{of}}\,{\text{incident}}\,{\text{medium}}$
${n_2} = \,{\text{refractive}}\,{\text{index}}\,{\text{of}}\,{\text{refracted}}\,{\text{medium}}$
${{\text{v}}_i}\,{\text{ = }}\,{\text{velocity}}\,{\text{of}}\,{\text{light}}\,{\text{in}}\,{\text{incident}}\,{\text{medium}}$
${{\text{v}}_r}\,{\text{ = }}\,{\text{velocity}}\,{\text{of}}\,{\text{light}}\,{\text{in}}\,{\text{refracted}}\,{\text{medium}}$
The above equation gives the relation between Snell’s law and refractive indices of medium.

Note:
 It is important to understand from which the light travels and to which media it enters. Keeping medium in mind we can easily differentiate between absolute and relative refractive index. Besides this, the medium of travel is very important in Snell’s law. We should remember that velocity and angle of a media are directly proportional while refractive index of that media is indirectly proportional.