The unit of dispersive power is

Options

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

Answer

To solve the question regarding the unit of dispersive power, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Dispersive Power**:
Dispersive power (W) is defined as the measure of how much the refractive index of a material varies with wavelength. It is calculated using the formula:
\[ W = \frac{\mu_V - \mu_R}{\mu - 1} \]
where:
- \(\mu_V\) is the refractive index for violet light,
- \(\mu_R\) is the refractive index for red light,
- \(\mu\) is the refractive index of the material.

2. **Identify the Units in the Formula**:
In the formula for dispersive power, all the terms (\(\mu_V\), \(\mu_R\), and \(\mu\)) represent refractive indices. The refractive index is a dimensionless quantity, meaning it does not have any units.

3. **Analyze the Formula**:
Since both the numerator (\(\mu_V - \mu_R\)) and the denominator (\(\mu - 1\)) consist of refractive indices, they are both unitless. Therefore, the entire expression for dispersive power is also unitless.

4. **Conclusion**:
Since dispersive power is derived from a ratio of unitless quantities, it also has no units. Thus, the unit of dispersive power is "no unit" or "unitless".

### Final Answer:
The unit of dispersive power is unitless.