In a double-slit diffraction experiment, the number of interference fringes within the central diffraction maximum can be increased by

Options

A. Increasing the wavelength
B. Decreasing the wavelength
C. Decreasing the slit separation
D. Decreasing the slit width

Answer

To solve the problem of increasing the number of interference fringes within the central diffraction maximum in a double-slit diffraction experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Conditions for Interference and Diffraction**:
- The condition for constructive interference in a double-slit experiment is given by:
\[ d \sin \theta = n \lambda \]
where \(d\) is the distance between the slits, \(n\) is the order of the fringe, and \(\lambda\) is the wavelength of light used.

2. **Understand the Diffraction Condition**:
- The condition for the first minimum in single-slit diffraction is given by:
\[ a \sin \theta = \lambda \]
where \(a\) is the width of the slit.

3. **Relate the Two Conditions**:
- To find the number of interference fringes (\(n\)) within the central maximum, we can combine the two equations:
\[ d \left(\frac{\lambda}{a}\right) = n \lambda \]
- Simplifying this gives:
\[ n = \frac{d}{a} \]
- This shows that the number of interference fringes is directly proportional to the slit separation \(d\) and inversely proportional to the slit width \(a\).

4. **Identify Ways to Increase \(n\)**:
- To increase \(n\), we can:
- **Increase the slit separation \(d\)**: This will increase the number of fringes.
- **Decrease the slit width \(a\)**: This will also increase the number of fringes since \(n\) is inversely proportional to \(a\).

5. **Conclusion**:
- Therefore, to increase the number of interference fringes within the central diffraction maximum, we can either increase the distance between the slits or decrease the width of the slits.

### Final Answer:
The number of interference fringes within the central diffraction maximum can be increased by decreasing the slit width.

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