In Young's double-slit experiment, the path difference refers to the difference in the distance traveled by light waves from the two slits to a particular point on the screen where the interference pattern is observed. The path difference determines the phase relationship between the waves arriving at that point and directly influences the resulting interference pattern.
The interference pattern arises due to the superposition of the waves from the two slits. When the path difference is an integer multiple of the wavelength of the light (λ), the waves are said to be in phase and constructive interference occurs. In this case, the amplitudes of the waves add up, resulting in bright fringes or regions of maximum intensity in the interference pattern.
On the other hand, when the path difference is a half-integer multiple of the wavelength (λ/2), the waves are out of phase and destructive interference occurs. In this case, the amplitudes of the waves cancel out, resulting in dark fringes or regions of minimum intensity in the interference pattern.
Therefore, there is a direct relationship between the path difference and the intensity of light in Young's double-slit experiment. When the path difference is such that the waves are in phase, constructive interference leads to higher intensity (bright fringes), and when the path difference is such that the waves are out of phase, destructive interference leads to lower intensity (dark fringes) in the interference pattern. The specific pattern of bright and dark fringes is determined by the precise values of the path differences between the two slits and the point of observation on the screen.