The Cauchy’s dispersion formula is

Options

A. (a)`n=A + Blambda^(-2) + Clambda^(-4)`
B. (b)`n=A + Blambda^(2) + Clambda^(-4)`
C. (c)`n=A + Blambda^(-2) + Clambda^(4)`
D. (d)`n=A + Blambda^(2) + Clambda^(4)`

Answer

### Step-by-Step Solution:

1. **Understanding Cauchy's Dispersion Formula**:
- Cauchy's dispersion formula is used to describe how the refractive index of a material varies with the wavelength of light. It is particularly useful for most transparent substances.

2. **Identifying the Formula**:
- The general form of Cauchy's dispersion formula can be expressed as:
\[ n(\lambda) = A + \frac{B}{\lambda^2} + \frac{C}{\lambda^4} \]
- Here, \( n \) is the refractive index, \( \lambda \) is the wavelength of light, and \( A \), \( B \), and \( C \) are constants specific to the material.

3. **Analyzing the Given Options**:
- The question provides multiple-choice options. We need to identify which one correctly represents Cauchy's dispersion formula.

4. **Comparing with Options**:
- From the derived formula, we can see that the correct representation of Cauchy's dispersion formula matches the form \( A + \frac{B}{\lambda^2} + \frac{C}{\lambda^4} \).
- If option (a) is presented as \( A + B \lambda^{-2} + C \lambda^{-4} \), then it is the correct option.

5. **Conclusion**:
- After analyzing the options, we conclude that the correct representation of Cauchy's dispersion formula is indeed found in option (a).

### Final Answer:
The Cauchy’s dispersion formula is given by:
\[ n(\lambda) = A + \frac{B}{\lambda^2} + \frac{C}{\lambda^4} \]