Question

If $ {\varepsilon}_0 $ and $ {\mu}_0 $ are the electric permittivity and magnetic permeability in a free space, $ \varepsilon $ and $\mu $ are the corresponding quantities in medium, the index and refraction of the medium is

• A. $\sqrt{ \frac{ {\varepsilon}_0 {\mu}_0}{\varepsilon \mu }}$
• B. $\sqrt{ \frac{\varepsilon \mu}{{\varepsilon}_0 {\mu}_0}}$
• C. $\sqrt{ \frac{{\varepsilon}_0 \mu }{\varepsilon {\mu}_0}}$
• D. $\sqrt{ \frac{\varepsilon}{{\varepsilon}_0}}$

Answer 1

The Correct Option is B

To determine the refractive index of a medium, we can use the relationship between the electric permittivity and magnetic permeability of free space and the corresponding values in the medium.

The refractive index \( n \) of a medium is defined by the square root of the ratio of the product of permittivity and permeability in the medium to that in free space. The formula is given as:

n = \sqrt{ \frac{\varepsilon \mu}{{\varepsilon}_0 {\mu}_0}}

Where:

• \varepsilon is the electric permittivity of the medium.
• \mu is the magnetic permeability of the medium.
• \varepsilon_0 is the electric permittivity of free space.
• \mu_0 is the magnetic permeability of free space.

By substituting these values into the formula, we derive the expression for the refractive index of the medium as:

n = \sqrt{ \frac{\varepsilon \mu}{{\varepsilon}_0 {\mu}_0}}

Comparing this with the given options, the correct answer is:

\sqrt{ \frac{\varepsilon \mu}{{\varepsilon}_0 {\mu}_0}}

This is option 2, which accurately represents the relationship between the permittivity and permeability of the medium compared to free space, thereby describing the refractive index.