Final answer:
In single-slit diffraction patterns, a larger slit width leads to a narrower pattern. The envelope of a double-slit diffraction pattern is determined by the single-slit diffraction pattern, whereas the sharp peaks within that envelope result from constructive interference between the two slits.
Step-by-step explanation:
Effects of Slit Width on Single and Double-Slit Diffraction Patterns
When discussing single slit diffraction patterns, as the aperture or slit width a gets larger, the overall size of the diffraction pattern becomes narrower. This is because the angle for the first diffraction minimum is inversely proportional to the size of the slit - meaning a larger slit width results in a smaller angle, thereby narrowing the diffraction pattern. For single-slit diffraction, this will make the central maximum appear brighter and more defined, while the side maxima become less noticeable.
In the context of a double slit diffraction pattern, the diffraction pattern is made up of a series of bright and dark fringes. The 'envelope' of the pattern, meaning the overall shape and extent of the pattern, is determined by the single-slit diffraction pattern that each of the slits would produce individually. Consequently, the width of the slits is responsible for this envelope since it affects the diffraction pattern in the same way as described for a single slit.
The more defined peaks within the envelope, or the sharper bright fringes, in the double-slit diffraction pattern are caused by the interference of light emerging from the two slits. These fringes result from constructive interference, where the light waves are in phase and amplify each other. The distance between these slits, often noted as d, in conjunction with the wavelength of the light used and the order of the fringe, determines the positions of these maxima.