Question

Dielectric constant of a medium is 3 and its magnetic permeability \(\mu = 2\mu_0\). Find ratio of velocity of light in vacuum to velocity of light in medium :

• A. \(\sqrt{5}\)
• B. \(\sqrt{6}\)
• C. 2
• D. 3

Hint:

The refractive index of a material is not just determined by its dielectric properties but also its magnetic properties.
For non-magnetic materials, \(\mu_r \approx 1\), and the formula simplifies to the more common \(n = \sqrt{\epsilon_r}\). Always check if the material is magnetic.

Answer 1

The Correct Option is B

The speed of light in a medium is given by the formula: 

\(v = \frac{1}{\sqrt{\varepsilon \mu}}\),

where \(\varepsilon\) is the permittivity of the medium and \(\mu\) is the permeability of the medium. The speed of light in vacuum \(c\) is given by:

\(c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}}\),

where \(\varepsilon_0\) is the permittivity of free space and \(\mu_0\) is the permeability of free space.

We are given:

• Dielectric constant (\(\varepsilon_r\)) = 3, so \(\varepsilon = 3\varepsilon_0\).
• Magnetic permeability \(\mu = 2\mu_0\).

We need to find the ratio of the velocity of light in vacuum to that in the medium:

\(\frac{c}{v} = \frac{\sqrt{\varepsilon \mu}}{\sqrt{\varepsilon_0 \mu_0}}\)

Substitute the given values:

\(\frac{c}{v} = \sqrt{\frac{3\varepsilon_0 \cdot 2\mu_0}{\varepsilon_0 \cdot \mu_0}}\)

Simplifying further:

\(\frac{c}{v} = \sqrt{3 \times 2} = \sqrt{6}\)

Thus, the ratio of the velocity of light in vacuum to that in the medium is \(\sqrt{6}\).

The correct answer is:

\(\sqrt{6}\)