Question

What is the relation between optical density, refractive index and speed of light?

Answer 1

Hint: The speed of light in a given medium is inversely proportional to its refractive index. The speed of light in vacuum is a constant quantity. We can say that optical density is directly proportional to refractive index and inversely proportional to speed of light for that given medium.

Complete Answer:
Absolute refractive index is defined as the ratio of speed of light in vacuum to that in a given medium. It is represented as \[\mu \] and numerically \[\mu = \dfrac{{\text{c}}}{{\text{v}}}\] where c is speed of light in vacuum and v is speed of light in that given medium.
As speed of light in vacuum is constant and that is \[3 \times {10^8}{\text{m}}{{\text{s}}^{ - 1}}\] so, we can say that refractive index for a medium is inversely proportional to speed of light in that given medium. Thus, denser is the medium, lesser will be the speed of light as a denser medium has great refractive index value. A rarer medium has greater speed of light in it as for a rarer medium, its refractive index value is low.
We can also say the medium with a higher refractive index in which speed of light is less, such medium is known as optically denser medium and on the other hand, the medium in which the speed of light is more with lower refractive index, such medium is known as optically rarer medium.

Note: Refractive index of a medium with respect to refractive index of another medium is known as relative refractive index. When light passes from one medium to the other, the refractive index of medium 2 with respect to 1 is written as \[_1{\mu _2}\] and it can be given as:
\[_1{\mu _2} = \dfrac{{{\mu _2}}}{{{\mu _1}}} = \dfrac{{\left( {\dfrac{{\text{c}}}{{{{\text{v}}_2}}}} \right)}}{{\left( {\dfrac{{\text{c}}}{{{{\text{v}}_1}}}} \right)}} = \dfrac{{{{\text{v}}_1}}}{{{{\text{v}}_2}}}\] .