If the intensity of the waves obvserved by two coherent sources is 1. Then the intensity of resultant waves in constructive interferences will be:

Options

A. 21
B. 41
C. 1
D. None of the above

Answer

To solve the problem of finding the intensity of resultant waves in constructive interference when the intensity of waves observed by two coherent sources is given as 1, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Intensity and Amplitude**:
The intensity (I) of a wave is proportional to the square of its amplitude (A). This relationship can be expressed as:
\[ I \propto A^2 \]

2. **Identifying Intensities**:
Let the intensity of each coherent source be \( I_1 = 1 \) and \( I_2 = 1 \).

3. **Resultant Intensity in Constructive Interference**:
In constructive interference, the amplitudes of the waves add up. Therefore, the resultant amplitude \( A_r \) can be expressed as:
\[ A_r = A_1 + A_2 \]
Since the intensities are equal, we can denote the amplitude corresponding to intensity 1 as \( A \). Thus:
\[ A_1 = A \quad \text{and} \quad A_2 = A \]
Therefore,
\[ A_r = A + A = 2A \]

4. **Calculating Resultant Intensity**:
The resultant intensity \( I_r \) can now be calculated using the relationship between intensity and amplitude:
\[ I_r \propto (A_r)^2 = (2A)^2 = 4A^2 \]
Since \( A^2 \) corresponds to intensity 1, we have:
\[ I_r = 4 \times 1 = 4 \]

5. **Conclusion**:
Therefore, the intensity of the resultant waves in constructive interference will be:
\[ \boxed{4} \]