In Young’s experiment, if the amplitude of interferring waves are unequal then the :

Options

A. contrast in the fringes decreases
B. contrast in the fringes increase
C. number of fringes will increase
D. number of frings will decrease

Answer

To solve the question regarding Young's experiment and the effect of unequal amplitudes of interfering waves, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Intensity**:
- In wave optics, the intensity (I) of a wave is directly proportional to the square of its amplitude (A). This can be expressed as:
\[ I \propto A^2 \]

2. **Identifying the Amplitudes**:
- Let the amplitudes of the two interfering waves be \( A_1 \) and \( A_2 \). The corresponding intensities will be:
\[ I_1 = k A_1^2 \quad \text{and} \quad I_2 = k A_2^2 \]
where \( k \) is a proportionality constant.

3. **Calculating Maximum and Minimum Intensities**:
- The maximum intensity \( I_{max} \) when the waves interfere constructively is given by:
\[ I_{max} = I_1 + I_2 = k A_1^2 + k A_2^2 \]
- The minimum intensity \( I_{min} \) when the waves interfere destructively is given by:
\[ I_{min} = |I_1 - I_2| = |k A_1^2 - k A_2^2| \]

4. **Determining Contrast**:
- The contrast (C) of the interference pattern can be defined as the ratio of maximum intensity to minimum intensity:
\[ C = \frac{I_{max}}{I_{min}} = \frac{k(A_1^2 + A_2^2)}{|k(A_1^2 - A_2^2)|} \]
- This simplifies to:
\[ C = \frac{A_1^2 + A_2^2}{|A_1^2 - A_2^2|} \]

5. **Analyzing the Effect of Unequal Amplitudes**:
- If \( A_1 \) and \( A_2 \) are unequal, \( |A_1^2 - A_2^2| \) will be a non-zero value, leading to a finite contrast.
- The greater the difference in amplitudes, the lower the contrast, as the minimum intensity will be significantly less than the maximum intensity.

6. **Conclusion**:
- Therefore, if the amplitudes of the interfering waves are unequal, the contrast in the interference pattern decreases.

### Final Answer:
If the amplitudes of the interfering waves are unequal, the contrast in the interference pattern decreases.