Interference happens when wave displacements (amplitude = max displacement) add together algebraically in space and time. This is a fancy way of saying that if two waves/pulses/ripples meet, their amplitudes add up at a particular place and a particular moment. When two crests meet, we get – what a surprise, a BIG crest – interference is CONSTRUCTIVE. When a crest meets a trough, we get zero disturbance- DESTRUCTIVE interference. Easiest to see with circular water waves because the wavelengths are of the order of centimetres.
Diffraction is the spreading of a wave round an edge. There’s only a change in the wave direction at the edge of the gap(s). If we imagine (à la Huygens) that a plane wave consists of a infinite number of closely packed circular ripples, at the edge of the gap, there’s nowhere else for the wave energy to go except in a circle. NB: the most circular pattern is observed when the wavelength is the same size as the gap. This applies whatever wave type we think about. It explains sound diffraction around doorways, also radio wave diffraction in the Welsh hills, so even the Welsh get to watch the telly….Shorter wavelengths won’t diffract as well around large obstacles, so if the gap size is large compared to the wavelength, we don’t see much diffraction.
The thing to now get hold of is this. We can’t have one without the other. This means that diffraction can be observed in a double-slit interference pattern. Essentially, this is because each slit emits a diffraction pattern, and the diffraction patterns interfere with each other.
The shape of the diffraction pattern is determined by the width of the slits, while the shape of the interference pattern is determined by d, the distance between the slits. If W is much larger than d, the pattern will be dominated by interference effects; if W and d are about the same size the two effects will contribute equally to the fringe pattern. Generally what you see is a fringe pattern that has missing interference fringes; these fall at places where dark fringes occur in the diffraction pattern. So, put another way, we see the broad diffraction envelope and underneath it, the equally spaced interference fringes. When an interference fringe sits underneath a diffraction minimum, we can’t see it. These so-called missing orders are a favourite in exams.
This treatment is detailed, but worth some study, as is this Java applet from Walter Fendt which just illustrates single slit diffraction. You can vary both the slit width (narrow slit = more diffraction) and the wavelength (longer wavelength [redder] = broader pattern.