Phase Difference at the First Minimum of a Single Slit Diffraction Pattern

To understand the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit at the first minimum of a single slit diffraction pattern, let's break down the explanation into the following sections:

1. Single Slit Diffraction Pattern
When a beam of light passes through a narrow slit, it diffracts, creating a pattern of bright and dark regions on a screen placed behind the slit. This pattern is known as the single slit diffraction pattern.

2. Central Maximum
The central maximum is the brightest region in the diffraction pattern, which is located at the center. It occurs when the diffracted waves from all parts of the slit overlap constructively.

3. First Minimum
The first minimum is the region adjacent to the central maximum where the intensity of the diffracted light is at its minimum. At this point, the diffracted waves from different parts of the slit interfere destructively.

4. Huygen's Wavelets
According to Huygen's principle, every point on a wavefront acts as a source of secondary wavelets that spread out in all directions. In the case of a single slit diffraction, the wavefront is a straight line passing through the midpoint of the slit.

5. Phase Difference at the First Minimum
At the first minimum, the wavelets from the edge of the slit and the midpoint of the slit have to travel different distances to reach a particular point on the screen. This difference in path length leads to a phase difference between the two wavelets.

The phase difference at the first minimum can be calculated using the concept of path difference. The path difference is the difference in distance traveled by the two wavelets to reach a point on the screen. It can be given by:

Path Difference = d * sin(theta)

Where:
- d is the width of the slit
- theta is the angle between the line joining the midpoint of the slit and the point on the screen, and the normal to the screen

The phase difference can be calculated using the path difference and the wavelength of light. The phase difference is given by:

Phase Difference = (2π / λ) * Path Difference

Where:
- λ is the wavelength of light

6. Conclusion
At the first minimum of a single slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is determined by the path difference between the two wavelets. This path difference is a result of the different distances traveled by the wavelets to reach a point on the screen. By calculating the phase difference, we can understand the interference pattern observed in the diffraction pattern.