In Young's double-slit experiment, the interference pattern is created by light passing through two closely spaced slits. The distance between the interference fringes, also known as the fringe separation or fringe spacing, depends on the separation between the slits. Here's how the fringe separation is affected by the slit separation:
Smaller Slit Separation: When the separation between the slits is decreased, the fringe separation increases. In other words, the fringes become more widely spaced. This relationship is a consequence of the wave nature of light and can be understood using basic principles of interference. As the slits move closer together, the path difference between the waves from the two slits at a given point on the screen decreases. This leads to a wider spacing between the bright and dark fringes.
Larger Slit Separation: Conversely, when the separation between the slits is increased, the fringe separation decreases. The fringes become closer together, resulting in a narrower spacing between them. This occurs because the path difference between the waves from the slits at a given point on the screen increases as the slits move farther apart.
Now, regarding the disappearance of fringes, it is possible for the interference fringes to vanish under certain conditions:
Completely Destructive Interference: If the path difference between the waves from the two slits is such that they undergo complete destructive interference at all points on the screen, the fringes will disappear. This can happen when the slit separation is such that the path difference between the waves is equal to an integer multiple of the wavelength of the light. In this case, the waves cancel each other out, resulting in a uniform illumination across the screen.
Partial Destructive Interference: Fringes may also appear to be absent or less pronounced due to partial destructive interference. This occurs when the path difference between the waves is close to an integer multiple of the wavelength, but not exactly equal to it. The interference pattern becomes less distinct, and the fringes may appear weaker or even blend together, making them less noticeable.
It's important to note that the disappearance of fringes does not mean the absence of interference. Rather, it signifies a specific arrangement of the waves that leads to destructive interference and results in a different pattern or no pattern at all.
In summary, the fringe separation in Young's experiment is influenced by the separation between the slits. Decreasing the slit separation widens the fringes, while increasing the slit separation narrows them. Additionally, fringes can disappear either due to complete destructive interference or partial destructive interference, resulting in a uniform or less distinct pattern on the screen, respectively.