Question

The dielectric constant of mica is \[6\] , what is the velocity of light in this medium approximately?
$(A)1.2 \times {10^7}m/s$
$(B)5.0 \times {10^7}m/s$
$(C)1.2 \times {10^8}m/s$
$(D)3.0 \times {10^8}m/s$

Answer 1

Hint: First, the relation between the refractive index and the dielectric constant has to be included. Next to be noted that the refractive index of a material is the ratio of the velocity of the light in air to the velocity of the light through this material or medium.
From these relations, the velocity of light in this given medium can be found.

Formula used:
Refractive index, $n = \sqrt \varepsilon $ , $\varepsilon $ is the dielectric constant of mica.
And, $n = \dfrac{c}{v}$,
$c$ is the velocity of the light in air and $v$ is the velocity of the light through mica.
$\therefore \sqrt \varepsilon = \dfrac{c}{v}$

Complete step by step answer:
The relation between the dielectric constant and the refractive index of some medium or material is given by, $n = \sqrt \varepsilon $,
Let, $\varepsilon $ is the dielectric constant of mica.
And, $n$ is the Refractive index of this material.
We know that the refractive index is the ratio of the velocity of the light in air to the velocity of the light through this material or medium.
If $c$ is the velocity of the light in air and $v$ is the velocity of the light through mica,
Then, $n = \dfrac{c}{v}$
$\therefore \sqrt \varepsilon = \dfrac{c}{v}$
$ \Rightarrow v = \dfrac{c}{{\sqrt \varepsilon }}$
Given that, $\varepsilon = 6$ and we know $c = 3 \times {10^8}m/s$
$\therefore v = \dfrac{{3 \times {{10}^8}}}{{\sqrt 6 }}$
$ \Rightarrow v = 1.22 \times {10^8}$
So, the velocity of the light through mica is $1.22 \times {10^8}$, approximately $1.2 \times {10^8}m/s$

So, the correct answer is “Option C”.

Note: The dielectric constant can be the number of electrical potential energy, within the sort of induced polarization that keeps during a given volume of matter underneath the action of an electrical field. It's expressed because of the magnitude relation of the dielectric permittivity of the material to a vacuum or dry air.
Dielectric means an insulating or an awfully poor conductor of electrical current. Once dielectrics are kept in an electrical field, no current flows in them as a result of, in contrast to metals, they have no loosely bound, or free, electrons which will drift through the material.