The refractive index of a prism measured using three lines of a mercury vapour lamp. If `mu_1,mu_2 and mu_3` are the measured refractive indices for these green, blue and yellow lines respectively, then

Options

A. `mu_2 gt mu_3 gt mu_1`
B. `mu_2 gt mu_1 gt mu_3`
C. `mu_3 gt mu_2 gt mu_1`
D. `mu_1 gt mu_2 gt mu_3`

Explanation

To solve the problem, we need to understand the relationship between the refractive indices of the prism for different colors of light. The refractive index (μ) of a material is known to depend on the wavelength (λ) of the light passing through it.

### Step-by-Step Solution:

1. **Understanding the Wavelengths**:
- The three colors of light from the mercury vapor lamp are green, blue, and yellow.
- In the visible spectrum, the order of these colors from shortest to longest wavelength is: blue (shortest), green, and yellow (longest).

2. **Refractive Index and Wavelength Relationship**:
- The refractive index (μ) is inversely proportional to the square of the wavelength (λ). This relationship can be expressed as:
\[ μ = μ_0 + \frac{a}{λ^2} \]
- Here, \(μ_0\) is a constant and \(a\) is another constant that depends on the material.

3. **Comparing the Wavelengths**:
- Since blue light has the shortest wavelength, it will have the highest refractive index. Conversely, yellow light, which has the longest wavelength, will have the lowest refractive index.
- Therefore, we can establish the following relationships based on the wavelengths:
\[ λ_{\text{blue}} < λ_{\text{green}} < λ_{\text{yellow}} \]
- This implies:
\[ μ_{\text{blue}} > μ_{\text{green}} > μ_{\text{yellow}} \]
- In terms of the variables given in the question:
\[ μ_2 > μ_1 > μ_3 \]

4. **Final Conclusion**:
- Thus, we can conclude the relationship between the refractive indices:
\[ μ_2 > μ_1 > μ_3 \]