How does wave interference occur in single-slit diffraction?

Wave interference in single-slit diffraction occurs when waves passing through the slit spread out and overlap, creating an interference pattern.

In single-slit diffraction, a wavefront of light is incident on a barrier with a single narrow opening or slit. As the wavefront encounters the slit, it bends and spreads out in a process known as diffraction. This spreading out of the wavefront results in the formation of semi-circular or spherical wavefronts on the other side of the slit.

The key to understanding how wave interference occurs in this scenario lies in the principle of superposition. This principle states that when two or more waves overlap, the resultant wave is the sum of the displacements of the individual waves at each point. In the context of single-slit diffraction, each point on the wavefront can be considered as a source of secondary wavelets. These wavelets spread out in all directions and interfere with each other.

When the crests of two wavelets meet, they interfere constructively, resulting in a bright fringe. Conversely, when a crest from one wavelet meets a trough from another, they interfere destructively, resulting in a dark fringe. This alternating pattern of bright and dark fringes forms the interference pattern observed in single-slit diffraction.

The width of the slit also plays a crucial role in the interference pattern. A narrower slit results in more diffraction and a wider central bright fringe, while a wider slit results in less diffraction and a narrower central bright fringe. The angle of diffraction, which is the angle between the incident wavefront and the direction of the diffracted wave, is inversely proportional to the width of the slit.

In summary, wave interference in single-slit diffraction is a result of the diffraction of the wavefront at the slit and the subsequent overlapping of the secondary wavelets. The interference pattern is a direct consequence of the principle of superposition and is influenced by the width of the slit.