The Cauchy's formula is

Options

A. `n=A+ B lambda^(-2) + C lambda^(-4)`
B. `n=A+ B lambda^(-2)+C lambda^(4)`
C. `n=A+ B lambda^(2)+C lambda^(-4)`
D. `n=A+ B lambda^(2)+C lambda^(4)`

Explanation

To derive Cauchy's formula, we start with the understanding that it relates the refractive index (n) of a substance to the wavelength (λ) of light. The formula is typically expressed as:

\[ n(\lambda) = A + \frac{B}{\lambda^2} + \frac{C}{\lambda^4} \]

Where:
- \( n(\lambda) \) is the refractive index as a function of wavelength,
- \( A, B, C \) are constants specific to the material,
- \( \lambda \) is the wavelength of light.

### Step-by-Step Solution:

1. **Understanding the Formula**:
- Cauchy's formula describes how the refractive index changes with different wavelengths of light. It is particularly useful for understanding the dispersion of light in various materials.

2. **Identifying the Components**:
- In the formula, \( n \) represents the refractive index, while \( \lambda \) represents the wavelength of light. The constants \( A, B, \) and \( C \) are determined experimentally for different materials.

3. **Rearranging the Formula**:
- The formula can be rearranged to highlight the dependence on wavelength:
\[ n(\lambda) = A + B \cdot \lambda^{-2} + C \cdot \lambda^{-4} \]
- This shows that the refractive index decreases as the wavelength increases, which is typical for many materials.

4. **Application of the Formula**:
- To use Cauchy's formula, you would substitute the specific wavelength of light into the formula along with the constants for the material you are studying. This will give you the refractive index at that wavelength.

5. **Conclusion**:
- Cauchy's formula is a powerful tool in optics for predicting how light will behave as it travels through different media, especially in applications involving lenses and prisms.