If the eighth bright band due to light of wavelength `lamda_(1)` and coincides with ninth bright band from light of wavelength `lamda_(2)` is young's double slit experiment, then the possible wavelength of visible light are

Options

A. 400 nm and 450 nm
B. 425 nm and 400 nm
C. 400 nm and 425 nm
D. 450 nm and 400 nm

Explanation

To solve the problem, we need to analyze the conditions given in the Young's double-slit experiment. The problem states that the 8th bright band from light of wavelength \( \lambda_1 \) coincides with the 9th bright band from light of wavelength \( \lambda_2 \).

### Step-by-Step Solution:

1. **Understanding the Condition for Bright Bands**:
The position of the bright bands in a double-slit experiment is given by the formula:
\[ x = m \lambda \]
where \( m \) is the order of the bright band and \( \lambda \) is the wavelength of the light.

2. **Setting Up the Equations**:
For the 8th bright band of wavelength \( \lambda_1 \):
\[ x_1 = 8 \lambda_1 \]
For the 9th bright band of wavelength \( \lambda_2 \):
\[ x_2 = 9 \lambda_2 \]

3. **Equating the Positions**:
Since the two bands coincide, we can set the two equations equal to each other:
\[ 8 \lambda_1 = 9 \lambda_2 \]

4. **Finding the Ratio of Wavelengths**:
Rearranging the equation gives us:
\[ \frac{\lambda_1}{\lambda_2} = \frac{9}{8} \]

5. **Identifying Possible Wavelengths**:
We need to find values for \( \lambda_1 \) and \( \lambda_2 \) that satisfy this ratio. We will check the provided options to see which pair fits this ratio.

6. **Checking the Options**:
- **Option A**: \( \lambda_1 = 400 \, \text{nm}, \lambda_2 = 450 \, \text{nm} \)
\[ \frac{400}{450} = \frac{8}{9} \quad (\text{Not } \frac{9}{8}) \]
- **Option B**: \( \lambda_1 = 425 \, \text{nm}, \lambda_2 = 400 \, \text{nm} \)
\[ \frac{425}{400} = \frac{17}{16} \quad (\text{Not } \frac{9}{8}) \]
- **Option C**: \( \lambda_1 = 400 \, \text{nm}, \lambda_2 = 425 \, \text{nm} \)
\[ \frac{400}{425} = \frac{16}{17} \quad (\text{Not } \frac{9}{8}) \]
- **Option D**: \( \lambda_1 = 450 \, \text{nm}, \lambda_2 = 400 \, \text{nm} \)
\[ \frac{450}{400} = \frac{9}{8} \quad (\text{Matches } \frac{9}{8}) \]

7. **Conclusion**:
The only option that satisfies the condition \( \frac{\lambda_1}{\lambda_2} = \frac{9}{8} \) is Option D. Therefore, the possible wavelengths of visible light are:
\[ \lambda_1 = 450 \, \text{nm}, \quad \lambda_2 = 400 \, \text{nm} \]

### Final Answer:
The possible wavelengths of visible light are \( 450 \, \text{nm} \) and \( 400 \, \text{nm} \).