The intensity of interference waves in an interference pattern is same as `I_(0)`. The resultant intensity at any point of observation will be

Options

A. `I = 2I_(0)[1+cosphi]`
B. `I=I_(0)[1+cos phi]`
C. `I = [1+cos phi]/I_(0)`
D. `I=[1+cosphi]/(2I_(0))`

Answer

To solve the problem, we need to find the resultant intensity of interference waves when the intensities of the two waves are equal to \( I_0 \).

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The intensities of the two waves are equal: \( I_1 = I_2 = I_0 \).

2. **Use the Formula for Resultant Intensity**:
- The formula for the resultant intensity \( I_{\text{Net}} \) in an interference pattern is given by:
\[ I_{\text{Net}} = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi \]

3. **Substitute the Values**:
- Since \( I_1 = I_0 \) and \( I_2 = I_0 \), we can substitute these values into the formula:
\[ I_{\text{Net}} = I_0 + I_0 + 2\sqrt{I_0 I_0} \cos \phi \]

4. **Simplify the Expression**:
- This simplifies to:
\[ I_{\text{Net}} = 2I_0 + 2I_0 \cos \phi \]

5. **Factor Out Common Terms**:
- We can factor out \( 2I_0 \):
\[ I_{\text{Net}} = 2I_0 (1 + \cos \phi) \]

6. **Conclusion**:
- The resultant intensity at any point of observation is:
\[ I_{\text{Net}} = 2I_0 (1 + \cos \phi) \]

### Final Answer:
The resultant intensity at any point of observation will be \( 2I_0 (1 + \cos \phi) \).

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