The unit of refractive index is

Options

A. metre
B. degree
C. dioptre
D. it has no units

Answer

To determine the unit of refractive index, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Definition**:
- The refractive index (denoted as \( n \)) of a medium is defined as the ratio of the speed of light in a vacuum (or air) to the speed of light in that medium.

2. **Formula for Refractive Index**:
- The formula for refractive index is given by:
\[ n = \frac{c}{v} \]
where:
- \( n \) = refractive index
- \( c \) = speed of light in vacuum (or air)
- \( v \) = speed of light in the medium

3. **Units of Speed of Light**:
- The speed of light \( c \) is measured in meters per second (m/s).
- Similarly, the speed of light \( v \) in the medium is also measured in meters per second (m/s).

4. **Calculating the Units**:
- Since both \( c \) and \( v \) have the same unit (m/s), when we take the ratio \( \frac{c}{v} \), the units cancel out:
\[ n = \frac{\text{m/s}}{\text{m/s}} = 1 \]

5. **Conclusion**:
- Therefore, the refractive index is a dimensionless quantity, meaning it has no units.

### Final Answer:
The unit of refractive index is **unitless** (or it has no units).

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