Question

The ratio of the velocity of light in a vacuum to that in a medium is?

• A. \( \sqrt{\epsilon \mu} \)
• B. \( \frac{1}{\sqrt{\epsilon \mu}} \)
• C. \( \frac{\epsilon \mu}{2} \)
• D. \( \sqrt{\mu \epsilon} \)

Hint:

For problems involving the velocity of light in different media, remember the relation \( v = \frac{c}{\sqrt{\epsilon \mu}} \), which is useful when comparing light in vacuum versus light in a medium.

Answer 1

The Correct Option is B

The velocity of light in a vacuum is \( c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \), where \( \epsilon_0 \) is the permittivity of free space and \( \mu_0 \) is the permeability of free space. The velocity of light in a medium with relative permittivity \( \epsilon \) and relative permeability \( \mu \) is: \[ v = \frac{c}{\sqrt{\epsilon \mu}} \] Therefore, the ratio of the velocity of light in a vacuum to the velocity in the medium is: \[ \frac{c}{v} = \frac{1}{\sqrt{\epsilon \mu}} \]
Thus, the correct answer is (B) \( \frac{1}{\sqrt{\epsilon \mu}} \).