Why does the central maximum of a diffraction pattern is twice as long as any other?
Thank you
The math works out that way,
http://en.wikipedia.org/wiki/Diffraction
Qualitatively, and I suppose quantatively, too, the intensity of the undiffracted beam is higher than the diffracted beam since only a small portion of the light wave is bent.
The central maximum of a diffraction pattern is twice as long as any other because of a phenomenon called destructive interference.
To understand why, consider a diffraction pattern formed by a single slit. When light passes through a single slit, it spreads out and creates an interference pattern on a screen behind it. This pattern consists of a central maximum and a series of smaller, alternating bright and dark fringes on either side.
The width of each individual bright or dark fringe is determined by the wavelength of the light used and the size of the slit. The central maximum is the widest and brightest fringe in the pattern and is positioned at the center, directly opposite the slit.
The reason the central maximum is twice as long as any other fringe is because it is created by the overlapping of waves from the top and bottom edges of the slit. These waves interfere constructively, resulting in a larger bright region. However, all other fringes in the pattern are formed by the overlapping of waves from the top or bottom edge with the corresponding waves from the middle of the slit. In these regions, the waves interfere destructively, resulting in cancellation of some of the light and narrower fringes.
So, the central maximum in a diffraction pattern is twice as long as any other because it is formed by the constructive interference of waves from both the top and bottom edges of the slit.