In Young's double-slit experiment, a bright fringe is formed at the center of the screen due to constructive interference.
When a beam of light (or other wave-like particles) passes through the two slits in the barrier, it diffracts and spreads out as it emerges on the other side. The diffracted waves from each slit then overlap and interact with each other, creating an interference pattern on the screen.
At the center of the screen, the waves from both slits travel an equal distance and arrive in phase, meaning their peaks and troughs align. As a result, the waves reinforce each other, leading to constructive interference. This constructive interference produces a bright fringe at the center of the screen.
Mathematically, the condition for constructive interference at the center can be described as follows: When the path difference between the waves from the two slits is zero (or an integer multiple of the wavelength), the waves add up in phase, resulting in a bright fringe. This occurs because the crest of one wave aligns with the crest of the other wave, creating a stronger wave amplitude at that location.
In contrast, at other points on the screen, the waves from the two slits arrive with different path differences, leading to varying degrees of constructive or destructive interference, resulting in the formation of alternate bright and dark fringes in the interference pattern.
The presence of a bright fringe in the center of the screen is a characteristic feature of Young's double-slit experiment and is a consequence of the wave nature of light or other particles involved in the experiment.