# 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

Verified

281.4k+ views

**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.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Define absolute refractive index of a medium

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What are the measures one has to take to prevent contracting class 12 biology CBSE

Suggest some methods to assist infertile couples to class 12 biology CBSE

Trending doubts

The ray passing through the of the lens is not deviated class 10 physics CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

What is the nlx method How is it useful class 11 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What is the difference between anaerobic aerobic respiration class 10 biology CBSE