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

Options

A. `(x)/(2)`
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 Refractive Index**:
The refractive index \( \mu \) of a medium is defined as the ratio of the speed of light in vacuum (or free space) \( c \) to the speed of light in the medium \( v \):
\[ \mu = \frac{c}{v} \]

2. **Rearrange the Formula**:
From the definition of refractive index, we can express the speed of light in the medium \( v \) as:
\[ v = \frac{c}{\mu} \]

3. **Identify the Distance**:
We are given that the distance \( x \) is the distance light travels in the medium.

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

5. **Substitute for Speed**:
Now substitute \( v = \frac{c}{\mu} \) into the time formula:
\[ t = \frac{x}{\frac{c}{\mu}} = x \cdot \frac{\mu}{c} \]

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

### Conclusion:
The final answer is:
\[ t = \frac{\mu x}{c} \]