The distance between the screen and the slits in the double-slit experiment can have a significant impact on the resulting interference pattern. Specifically, this distance affects the spacing and the overall scale of the pattern.
The key factor influenced by the screen-slit distance is the angular spacing between the fringes. This angular spacing, denoted as θ, determines the position of the bright and dark fringes on the screen. It is given by the formula:
θ = λ / d,
where λ is the wavelength of the incident light and d is the distance between the slits.
As you can see from the formula, the angular spacing is inversely proportional to the distance between the slits. Thus, if the screen-slit distance is increased, the angular spacing between the fringes decreases. This means that the interference pattern will appear more compressed on the screen, with the fringes being closer together.
On the other hand, if the screen-slit distance is decreased, the angular spacing between the fringes increases, resulting in wider spacing between the fringes on the screen.
It's important to note that changing the screen-slit distance does not affect the overall shape or characteristics of the interference pattern. The pattern remains a series of alternating bright and dark fringes, but the specific spacing between these fringes is influenced by the distance between the screen and the slits.
In summary, the distance between the screen and the slits determines the angular spacing between the interference fringes. Increasing the distance leads to narrower spacing, while decreasing the distance results in wider spacing between the fringes.