How does refractive (µ) of a material vary with respect to wavelength (`lambda`)? A and B are constants

Options

A. µ=`A+(B)/(lambda^(2))`
B. µ=`A+Blambda^(2)`
C. µ=`A+(B)/(lambda)`
D. µ=`A+Blambda`

Explanation

To determine how the refractive index (µ) of a material varies with respect to wavelength (λ), we can use Cauchy's formula, which provides a mathematical relationship between these two quantities. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
Cauchy's formula states that the refractive index (µ) of a material can be expressed as a function of the wavelength (λ). The general form of Cauchy's equation is:
\[ \mu = A + \frac{B}{\lambda^2} \]
where A and B are constants specific to the material.

2. **Identifying the Variables**:
- µ: Refractive index of the material.
- λ: Wavelength of light.
- A and B: Constants that depend on the specific material.

3. **Analyzing the Equation**:
From the equation, we can see that:
- As the wavelength (λ) increases, the term \(\frac{B}{\lambda^2}\) decreases because λ is in the denominator and squared.
- Therefore, the refractive index (µ) decreases as the wavelength increases.

4. **Conclusion**:
The refractive index (µ) is inversely related to the square of the wavelength (λ). This means that shorter wavelengths (like blue light) will have a higher refractive index compared to longer wavelengths (like red light).

### Final Answer:
The refractive index (µ) of a material varies with respect to wavelength (λ) according to the equation:
\[ \mu = A + \frac{B}{\lambda^2} \]
where A and B are constants.

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