The unit of dispersive power is

Options

A. Radan
B. Diopter
C. Metre
D. Unitless

Answer

To determine the unit of dispersive power, we need to analyze the formula given for dispersive power (ω):

1. **Understanding the Formula**:
The dispersive power (ω) is defined as:
\[ \omega = \frac{\Delta V - \Delta R}{\Delta} \]
where:
- \(\Delta V\) is the deviation produced by violet light,
- \(\Delta R\) is the deviation produced by red light,
- \(\Delta\) is the deviation produced by mean yellow light.

2. **Identifying the Terms**:
- \(\Delta V\) and \(\Delta R\) are both angles of deviation, measured in degrees or radians.
- \(\Delta\) is also an angle of deviation, measured in the same units.

3. **Calculating the Units**:
Since all the terms in the formula are angles, we can express them in terms of their units:
- The unit of \(\Delta V\) is degrees (°) or radians (rad).
- The unit of \(\Delta R\) is also degrees (°) or radians (rad).
- The unit of \(\Delta\) is similarly degrees (°) or radians (rad).

4. **Simplifying the Expression**:
When we substitute the units into the formula:
\[ \omega = \frac{\text{(angle in degrees or radians)} - \text{(angle in degrees or radians)}}{\text{(angle in degrees or radians)}} \]
The units of angles in the numerator and denominator cancel out.

5. **Conclusion**:
Since the units cancel out, we find that the dispersive power (ω) is dimensionless. Therefore, the unit of dispersive power is:

**Answer**: Dimensionless (no unit).

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