Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is:

Options

A. `16/9`
B. `4/3`
C. `7/1`
D. `49/1`

Explanation

To solve the problem of finding the ratio of intensities of the bright and dark parts of the resultant interference pattern created by two monochromatic light beams with intensities 16 and 9 units, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Intensities**:
Let the intensities of the two light beams be:
- \( I_1 = 16 \) units
- \( I_2 = 9 \) units

2. **Calculate the Maximum Intensity (\( I_{max} \))**:
The formula for the maximum intensity in interference is given by:
\[ I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2 \]
First, calculate \( \sqrt{I_1} \) and \( \sqrt{I_2} \):
\[ \sqrt{I_1} = \sqrt{16} = 4 \]
\[ \sqrt{I_2} = \sqrt{9} = 3 \]
Now substituting these values into the formula:
\[ I_{max} = (4 + 3)^2 = 7^2 = 49 \]

3. **Calculate the Minimum Intensity (\( I_{min} \))**:
The formula for the minimum intensity in interference is given by:
\[ I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2 \]
Using the values calculated earlier:
\[ I_{min} = (4 - 3)^2 = 1^2 = 1 \]

4. **Calculate the Ratio of Maximum to Minimum Intensity**:
Now, we can find the ratio of the maximum intensity to the minimum intensity:
\[ \frac{I_{max}}{I_{min}} = \frac{49}{1} = 49 \]

5. **Final Result**:
Therefore, the ratio of intensities of the bright and dark parts of the resultant pattern is:
\[ \text{Ratio} = 49:1 \]