The path difference between two interfering light waves meeting at a point on the screen is `((87)/(2))lamda`. The band obtained at that point is

Options

A. 87th bright band
B. 87th dark band
C. 44th dark bannd
D. 44th light band

Explanation

To solve the problem of determining the type of band formed at a point on the screen where the path difference between two interfering light waves is given as \(\frac{87}{2} \lambda\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Path Difference**: The path difference (\(\Delta x\)) between two waves can determine whether the resulting interference at a point is constructive (bright band) or destructive (dark band).

2. **Identify Conditions for Bright and Dark Bands**:
- For **bright bands**, the path difference is given by:
\[ \Delta x = m \lambda \quad (m = 0, 1, 2, \ldots) \]
- For **dark bands**, the path difference is given by:
\[ \Delta x = \left( m + \frac{1}{2} \right) \lambda \quad (m = 0, 1, 2, \ldots) \]

3. **Given Path Difference**: The problem states that the path difference is:
\[ \Delta x = \frac{87}{2} \lambda \]

4. **Determine the Value of \(m\)**:
- To check if this corresponds to a bright or dark band, we can express \(\frac{87}{2} \lambda\) in terms of the two conditions:
- For bright bands: \(m = \frac{87}{2}\) (not an integer)
- For dark bands: Set \(\Delta x = \left( n + \frac{1}{2} \right) \lambda\):
\[ \frac{87}{2} = n + \frac{1}{2} \]
Rearranging gives:
\[ n = \frac{87}{2} - \frac{1}{2} = \frac{86}{2} = 43 \]

5. **Conclusion**:
- Since \(n\) is an integer (43), this indicates that the path difference corresponds to a dark band. Therefore, the band obtained at that point is the **44th dark band**.

### Final Answer:
The band obtained at that point is the **44th dark band**.

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