Question

For a transparent medium relative permeability and permittivity, $\mu_ r$ and $\epsilon_{r}$ are $1.0$ and $1.44$ respectively. The velocity of light in this medium would be,

• A. 2.5 × 10$^8$ m/s
• B. 3 × 10$^8$ m/s
• C. 2.08 × 10$^8$ m/s
• D. 4.32 × 10$^8$ m/s

Answer 1

The Correct Option is A

To determine the velocity of light in a medium, we use the relationship between the speed of light, relative permeability (\mu_r), and relative permittivity (\epsilon_r) of the medium. The equation for the speed of light (v) in a medium is given by the formula:

$$ v = \frac{c}{\sqrt{\mu_r \epsilon_r}} $$

where:

• c is the speed of light in a vacuum, approximately 3 \times 10^8 m/s.
• \mu_r is the relative permeability of the medium.
• \epsilon_r is the relative permittivity of the medium.

Given that \mu_r = 1.0 and \epsilon_r = 1.44, we substitute these values into the formula:

$$ v = \frac{3 \times 10^8}{\sqrt{1.0 \times 1.44}} $$

Calculating the denominator:

$$ \sqrt{1.0 \times 1.44} = \sqrt{1.44} = 1.2 $$

Substitute back to find the speed:

$$ v = \frac{3 \times 10^8}{1.2} = 2.5 \times 10^8 \text{ m/s} $$

Therefore, the velocity of light in this medium is 2.5 \times 10^8 m/s.

The correct answer is 2.5 × 10⁸ m/s.