If d is the real path length, then the optical path length (in medium of refractive index `mu`) is equal to

Options

A. `mud`
B. `d/mu`
C. `mu/d`
D. `1/(mud)`

Answer

To find the optical path length in a medium with a refractive index \( \mu \) when the real path length is \( d \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Refractive Index**:
The refractive index \( \mu \) of a medium is defined as the ratio of the speed of light in vacuum \( c \) to the speed of light in the medium \( v \):
\[ \mu = \frac{c}{v} \]

2. **Determine the Speed of Light in the Medium**:
From the definition of refractive index, we can express the speed of light in the medium:
\[ v = \frac{c}{\mu} \]

3. **Calculate the Time Taken in the Medium**:
The time \( t \) taken for light to travel a distance \( d \) in the medium can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Speed}} = \frac{d}{v} \]
Substituting \( v \) from step 2:
\[ t = \frac{d}{\frac{c}{\mu}} = \frac{d \mu}{c} \]

4. **Calculate the Optical Path Length**:
The optical path length is defined as the distance light would travel in vacuum in the same time \( t \). Therefore, if light travels a distance \( \mu d \) in vacuum in the same time \( t \):
\[ \text{Optical Path Length} = \mu d \]

5. **Conclusion**:
Thus, the optical path length in a medium of refractive index \( \mu \) for a real path length \( d \) is:
\[ \text{Optical Path Length} = \mu d \]

### Final Answer:
The optical path length (in a medium of refractive index \( \mu \)) is equal to \( \mu d \).

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