Final answer:
To produce a sustained interference pattern, light sources must be coherent and maintain a consistent phase relationship, with points spaced about a wavelength apart. In a double-slit experiment, this results in constructive and destructive interference leading to fringe patterns.
Step-by-step explanation:
To produce a sustained interference pattern by light waves from multiple sources, certain conditions must be satisfied. First, the light sources must be coherent; that is, they must have a constant phase difference and the same frequency. This coherence allows the waves to interact consistently over time, producing a stable pattern. Secondly, a consistent phase relationship between the waves must be maintained, which is achieved when the waves are emitted from points spaced apart by about the wavelength of light.
In a typical double-slit experiment, light passes through two narrow slits, with each slit acting as a point source for the waves. These waves then interfere with each other constructively or destructively, depending on the path difference between them, to create a series of bright and dark fringes on a screen. Constructive interference occurs when the path-length difference is an integral multiple of the wavelength, while destructive interference occurs when the path difference is a half-integral multiple of the wavelength. The result is a predictable pattern of fringes dependent on the light's wavelength and the geometry of the setup.