In Young's double-slit experiment, the interference pattern arises from the superposition of waves from two coherent sources, such as light passing through two slits. The position of the fringes in the pattern is determined by the wavelength of the light and the geometry of the setup.
The fringe spacing, or the distance between adjacent bright or dark fringes, is given by the equation:
dλ = mλ
where d is the distance between the two slits, λ is the wavelength of the light, and m is the order of the fringe.
In this equation, it's clear that the fringe spacing is directly proportional to the wavelength of the light. Therefore, light with a longer wavelength, such as red light, will have a larger fringe spacing compared to light with a shorter wavelength, such as violet light.
The reason for this behavior is related to the wave nature of light. When light passes through the slits, it diffracts and forms an interference pattern on the screen. The spacing between the slits determines the angle at which the light waves spread out after passing through the slits.
As the wavelength increases, the diffraction pattern expands, resulting in wider fringe spacing. Red light has a longer wavelength than violet light, so its diffraction pattern is more spread out, and the fringes are farther apart from the central bright fringe. Violet light, with its shorter wavelength, produces a more closely spaced interference pattern.
Therefore, in Young's double-slit experiment, the red light is farther from the central bright fringe than violet light due to the differences in their respective wavelengths and the resulting interference pattern.