The intensity of light emerging from one slit is nine times than that from the other slit in Young's double sit interference set up. The ratio of maximum intensity to minimum intensity in the fringe pattern is

Options

A. `2:1`
B. `4:1`
C. `6:1`
D. `8:1`

Answer

To solve the problem, we need to find the ratio of maximum intensity to minimum intensity in a Young's double slit interference setup where the intensity of light from one slit is nine times that from the other slit.

### Step-by-Step Solution:

1. **Define the Intensities**:
Let the intensity of light from slit 1 be \( I_1 \) and from slit 2 be \( I_2 \). According to the problem, we have:
\[ I_1 = I \quad \text{and} \quad I_2 = 9I \]

2. **Relate Intensity to Amplitude**:
The intensity of a wave is proportional to the square of its amplitude. Therefore, we can express the amplitudes \( A_1 \) and \( A_2 \) in terms of the intensities:
\[ A_1 = \sqrt{I_1} = \sqrt{I} \quad \text{and} \quad A_2 = \sqrt{I_2} = \sqrt{9I} = 3\sqrt{I} \]

3. **Calculate Maximum Amplitude**:
The maximum amplitude \( A_{\text{max}} \) occurs when the waves from both slits are in phase:
\[ A_{\text{max}} = A_1 + A_2 = \sqrt{I} + 3\sqrt{I} = 4\sqrt{I} \]

4. **Calculate Minimum Amplitude**:
The minimum amplitude \( A_{\text{min}} \) occurs when the waves are out of phase:
\[ A_{\text{min}} = A_2 - A_1 = 3\sqrt{I} - \sqrt{I} = 2\sqrt{I} \]

5. **Calculate Maximum and Minimum Intensities**:
The maximum intensity \( I_{\text{max}} \) and minimum intensity \( I_{\text{min}} \) can be calculated from the maximum and minimum amplitudes:
\[ I_{\text{max}} = A_{\text{max}}^2 = (4\sqrt{I})^2 = 16I \]
\[ I_{\text{min}} = A_{\text{min}}^2 = (2\sqrt{I})^2 = 4I \]

6. **Calculate the Ratio of Maximum to Minimum Intensity**:
Finally, we can find the ratio of maximum intensity to minimum intensity:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{16I}{4I} = 4 \]

### Final Answer:
The ratio of maximum intensity to minimum intensity in the fringe pattern is \( 4:1 \).