In Young's double-slit experiment, two cohernet sources of different intensites are used to make interference pattern. Ratio of the maximum to minimum intensity of pattern is found to be 25. What will be ratio of intensities of sources?

Options

A. `625:1`
B. `9:4`
C. `25:1`
D. `5:1`

Explanation

To solve the problem, we need to find the ratio of the intensities of two coherent sources used in Young's double-slit experiment, given that the ratio of the maximum to minimum intensity of the interference pattern is 25.

### Step-by-Step Solution:

1. **Understanding the Problem**:
In Young's double-slit experiment, we have two coherent sources of light with intensities \( I_1 \) and \( I_2 \). The maximum intensity \( I_{max} \) and minimum intensity \( I_{min} \) in the interference pattern can be expressed in terms of these intensities.

2. **Formulas for Maximum and Minimum Intensity**:
The formulas for maximum and minimum intensity are:
\[ I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2 \]
\[ I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2 \]

3. **Setting Up the Ratio**:
We are given that the ratio of maximum to minimum intensity is 25:
\[ \frac{I_{max}}{I_{min}} = 25 \]
Substituting the expressions for \( I_{max} \) and \( I_{min} \):
\[ \frac{(\sqrt{I_1} + \sqrt{I_2})^2}{(\sqrt{I_1} - \sqrt{I_2})^2} = 25 \]

4. **Taking Square Roots**:
Taking the square root of both sides gives:
\[ \frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}} = 5 \]

5. **Cross Multiplying**:
Cross-multiplying leads to:
\[ \sqrt{I_1} + \sqrt{I_2} = 5(\sqrt{I_1} - \sqrt{I_2}) \]
Expanding the right side:
\[ \sqrt{I_1} + \sqrt{I_2} = 5\sqrt{I_1} - 5\sqrt{I_2} \]

6. **Rearranging the Equation**:
Rearranging gives:
\[ \sqrt{I_1} + 5\sqrt{I_2} = 5\sqrt{I_1} - \sqrt{I_2} \]
Combining like terms:
\[ 6\sqrt{I_2} = 4\sqrt{I_1} \]

7. **Finding the Ratio**:
Dividing both sides by \( \sqrt{I_2} \) and \( \sqrt{I_1} \):
\[ \frac{\sqrt{I_1}}{\sqrt{I_2}} = \frac{6}{4} = \frac{3}{2} \]
Squaring both sides gives:
\[ \frac{I_1}{I_2} = \left(\frac{3}{2}\right)^2 = \frac{9}{4} \]

### Final Answer:
The ratio of the intensities of the two sources is:
\[ \frac{I_1}{I_2} = \frac{9}{4} \]