Question

When light propagates through a material medium of relative permittivity єr, and relative permeability єr, the velocity of light, v is given by (c - velocity of light in vacuum)

• A. \(v=c\)
• B. \(v = \sqrt\frac{µ_r}{∈_r}\)
• C. \(v = \sqrt\frac{∈_r}{µ_r}\)
• D. \(v = \frac{c}{\sqrt{∈_rµ_r}}\)

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The velocity of electromagnetic waves (like light) in any medium depends on the electrical and magnetic properties of that medium, namely permittivity (\(\epsilon\)) and permeability (\(\mu\)).
Key Formula or Approach:
The velocity of light in vacuum is:
\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]
The velocity of light in a medium is:
\[ v = \frac{1}{\sqrt{\mu \epsilon}} \]
where \(\epsilon = \epsilon_0 \epsilon_r\) and \(\mu = \mu_0 \mu_r\).
Step 2: Detailed Explanation:
Substituting the expressions for \(\epsilon\) and \(\mu\) into the formula for \(v\):
\[ v = \frac{1}{\sqrt{(\mu_0 \mu_r)(\epsilon_0 \epsilon_r)}} \]
Rearranging the terms inside the square root:
\[ v = \frac{1}{\sqrt{\mu_0 \epsilon_0} \cdot \sqrt{\mu_r \epsilon_r}} \]
Since \(\frac{1}{\sqrt{\mu_0 \epsilon_0}} = c\), we can substitute it:
\[ v = \frac{c}{\sqrt{\mu_r \epsilon_r}} \]
Step 3: Final Answer:
The velocity of light in the medium is \(v = \frac{c}{\sqrt{\epsilon_r\mu_r}}\).