In Young's double slit experiment using sodium light (`lamda=5898Å`) 92 fringes are seen if given colour `(lamda=5461Å)` is used how many fringes will be seen

Options

A. 62
B. 67
C. 85
D. 99

Explanation

To solve the problem, we will use the relationship between the number of fringes observed in Young's double slit experiment and the wavelengths of the light used.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We are given that 92 fringes are seen with sodium light of wavelength \( \lambda_1 = 5898 \, \text{Å} \).
- We need to find out how many fringes \( n_2 \) will be seen when the wavelength is changed to \( \lambda_2 = 5461 \, \text{Å} \).

2. **Using the Formula**:
- The number of fringes \( n \) is directly proportional to the wavelength \( \lambda \). The relationship can be expressed as:
\[ \frac{n_1}{n_2} = \frac{\lambda_1}{\lambda_2} \]
- Rearranging this gives:
\[ n_2 = n_1 \cdot \frac{\lambda_2}{\lambda_1} \]

3. **Substituting the Values**:
- Here, \( n_1 = 92 \), \( \lambda_1 = 5898 \, \text{Å} \), and \( \lambda_2 = 5461 \, \text{Å} \).
- Plugging in the values:
\[ n_2 = 92 \cdot \frac{5461}{5898} \]

4. **Calculating \( n_2 \)**:
- First, calculate the fraction:
\[ \frac{5461}{5898} \approx 0.926 \]
- Now, multiply by 92:
\[ n_2 \approx 92 \cdot 0.926 \approx 85.5 \]
- Since the number of fringes must be a whole number, we round \( n_2 \) to the nearest whole number:
\[ n_2 \approx 86 \]

5. **Final Answer**:
- Therefore, the number of fringes that will be seen with the given color is approximately **86**.