If `mu` is the permeability and `in` is the permittivity then `(1)/(sqrt(mu in))` is equal to

Options

A. Speed of sound
B. Speed of light in vaccum
C. Speed of sound in medium
D. Speed of light in medium

Answer

To solve the problem, we need to relate the quantities given: permeability (μ) and permittivity (ε). We are asked to find the expression for \( \frac{1}{\sqrt{\mu \epsilon}} \).

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- Permeability (μ) is a measure of how much a material can support the formation of a magnetic field within itself.
- Permittivity (ε) is a measure of how much electric field is 'permitted' to pass through a material.

2. **Recall the Speed of Light Formula**:
- The speed of light in a vacuum (c) is given by the equation:
\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]
where \( \mu_0 \) is the permeability of free space (vacuum) and \( \epsilon_0 \) is the permittivity of free space (vacuum).

3. **Generalizing for Any Medium**:
- For a medium with permeability (μ) and permittivity (ε), the speed of light (v) in that medium can be expressed as:
\[ v = \frac{1}{\sqrt{\mu \epsilon}} \]

4. **Finding the Expression**:
- From the equation above, we can directly see that:
\[ \frac{1}{\sqrt{\mu \epsilon}} = v \]
- Here, \( v \) represents the speed of light in the medium characterized by the given permeability and permittivity.

5. **Conclusion**:
- Therefore, the final answer is:
\[ \frac{1}{\sqrt{\mu \epsilon}} = v \]
- Where \( v \) is the speed of light in the medium.