Sun light is diffracted through a circular aperture of diameter `0.1 mu m`. If diameter is slightly increased then

Options

A. Size of circular fringe will increase intensity decrease
B. Size of circular fringe will increase intensity increase
C. Size of circular fringe will decrease intensity decrease
D. Size of circular fringe will decrease intensity increase

Answer

To solve the problem, we need to analyze the diffraction pattern produced by a circular aperture and how it changes when the diameter of the aperture is increased.

### Step-by-Step Solution:

1. **Understanding Diffraction through a Circular Aperture**:
- When light passes through a circular aperture, it creates a diffraction pattern on a screen placed at a distance. This pattern consists of concentric bright and dark rings known as Airy patterns.

2. **Formula for the Radius of the First Dark Ring**:
- The radius of the first dark ring (R) in the diffraction pattern can be described by the formula:
\[ R = 1.22 \frac{\lambda D}{B} \]
where:
- \( \lambda \) is the wavelength of light,
- \( D \) is the distance from the aperture to the screen,
- \( B \) is the diameter of the aperture.

3. **Effect of Increasing the Diameter (B)**:
- If we slightly increase the diameter \( B \) of the aperture, we can see from the formula that \( R \) is inversely proportional to \( B \). This means that as \( B \) increases, \( R \) decreases.
- Therefore, the size of the circular fringe (the radius of the first dark ring) will decrease.

4. **Intensity of the Diffraction Pattern**:
- The intensity of the diffraction pattern is related to the amount of light passing through the aperture. When the diameter of the aperture is increased, more light rays can pass through.
- This results in an increase in the intensity of the light in the diffraction pattern.

5. **Conclusion**:
- From the analysis, we conclude that if the diameter of the circular aperture is slightly increased, the size of the circular fringe will decrease, and the intensity of the light will increase.
- Therefore, the correct option is:
- **Option 4: Size of Circular Fringe Will Decrease and Intensity Increase**.