In Young's double slit experiment, the ratio of maximum and minimum intensities in the fringe system is `9:1` the ratio of amplitudes of coherent sources is

Options

A. `9:1`
B. `3:1`
C. `2:1`
D. `1:1`

Explanation

To solve the problem, we need to find the ratio of the amplitudes of the coherent sources (A1 and A2) given the ratio of maximum and minimum intensities in Young's double slit experiment.

### Step-by-Step Solution:

1. **Understanding the Intensity Ratio**:
We are given that the ratio of maximum intensity (I_max) to minimum intensity (I_min) is 9:1. This can be expressed mathematically as:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = 9 \]

2. **Expression for Intensities**:
In Young's double slit experiment, the maximum and minimum intensities can be expressed in terms of the amplitudes (A1 and A2) of the two coherent sources:
\[ I_{\text{max}} = (A_1 + A_2)^2 \]
\[ I_{\text{min}} = (A_1 - A_2)^2 \]

3. **Setting Up the Equation**:
From the intensity ratio, we can write:
\[ \frac{(A_1 + A_2)^2}{(A_1 - A_2)^2} = 9 \]

4. **Taking Square Roots**:
Taking the square root of both sides gives:
\[ \frac{A_1 + A_2}{A_1 - A_2} = 3 \]

5. **Cross Multiplying**:
Cross multiplying gives us:
\[ A_1 + A_2 = 3(A_1 - A_2) \]

6. **Expanding and Rearranging**:
Expanding the right side:
\[ A_1 + A_2 = 3A_1 - 3A_2 \]
Rearranging the equation:
\[ A_1 + A_2 + 3A_2 = 3A_1 \]
\[ 4A_2 = 2A_1 \]

7. **Finding the Ratio**:
Dividing both sides by A2:
\[ \frac{A_1}{A_2} = 2 \]

8. **Final Ratio**:
Therefore, the ratio of the amplitudes A1 to A2 is:
\[ A_1 : A_2 = 2 : 1 \]

### Conclusion:
The ratio of amplitudes of the coherent sources is \( 2 : 1 \).