If c is the velocity of light in free space, the time taken by light to travel a distance x in a medium refractive index `mu` is

Options

A. `(x)/(c)`
B. `(mux)/(c)`
C. `(x)/(muc)`
D. `(c)/(mux)`

Explanation

To find the time taken by light to travel a distance \( x \) in a medium with refractive index \( \mu \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The speed of light in free space is denoted as \( c \).
- The refractive index of the medium is denoted as \( \mu \).
- The distance to be traveled by light in the medium is \( x \).

2. **Determine the Speed of Light in the Medium**:
- The speed of light in a medium is given by the formula:
\[ v = \frac{c}{\mu} \]
- Here, \( v \) is the speed of light in the medium, \( c \) is the speed of light in vacuum, and \( \mu \) is the refractive index of the medium.

3. **Use the Formula for Time**:
- The time taken \( t \) to travel a distance \( x \) is given by the formula:
\[ t = \frac{\text{Distance}}{\text{Speed}} \]
- Substituting the values we have:
\[ t = \frac{x}{v} \]

4. **Substitute the Speed of Light in the Medium**:
- Now, substitute \( v = \frac{c}{\mu} \) into the time formula:
\[ t = \frac{x}{\frac{c}{\mu}} \]
- This simplifies to:
\[ t = \frac{x \cdot \mu}{c} \]

5. **Final Expression**:
- Thus, the time taken by light to travel a distance \( x \) in a medium with refractive index \( \mu \) is:
\[ t = \frac{\mu x}{c} \]

### Final Answer:
The time taken by light to travel a distance \( x \) in a medium with refractive index \( \mu \) is \( \frac{\mu x}{c} \).

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