If ratio of amplitude of two interferring source is` 3 : 5`. Then ratio of intensity of maxima and minima in interference pattern will be:

Options

A. `25:16`
B. `5:3`
C. `16:1`
D. `25:9`

Answer

To solve the problem of finding the ratio of intensity of maxima and minima in an interference pattern given the amplitude ratio of two interfering sources as 3:5, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship Between Amplitude and Intensity**:
The intensity (I) of a wave is proportional to the square of its amplitude (A). This means:
\[ I \propto A^2 \]

2. **Define the Amplitudes**:
Let the amplitudes of the two waves be \( A_1 = 3k \) and \( A_2 = 5k \), where \( k \) is a constant.

3. **Calculate the Intensities**:
Using the relationship between intensity and amplitude:
\[ I_1 = k A_1^2 = k (3k)^2 = 9k^2 \]
\[ I_2 = k A_2^2 = k (5k)^2 = 25k^2 \]

4. **Finding the Ratio of Intensities**:
The ratio of the intensities \( I_1 \) and \( I_2 \) is:
\[ \frac{I_1}{I_2} = \frac{9k^2}{25k^2} = \frac{9}{25} \]

5. **Calculating Maximum Intensity**:
The maximum intensity \( I_{\text{max}} \) when two waves interfere constructively is given by:
\[ I_{\text{max}} = (A_1 + A_2)^2 = (3k + 5k)^2 = (8k)^2 = 64k^2 \]

6. **Calculating Minimum Intensity**:
The minimum intensity \( I_{\text{min}} \) when two waves interfere destructively is given by:
\[ I_{\text{min}} = (A_1 - A_2)^2 = (3k - 5k)^2 = (-2k)^2 = 4k^2 \]

7. **Finding the Ratio of Maximum to Minimum Intensity**:
Now, we find the ratio of maximum intensity to minimum intensity:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{64k^2}{4k^2} = \frac{64}{4} = 16 \]

8. **Final Result**:
Therefore, the ratio of intensity of maxima to minima is:
\[ I_{\text{max}} : I_{\text{min}} = 16 : 1 \]