Two different beams of same frequency light passed through the double slit We all know that when one beam of discrete frequency passes through the double slit makes an interference pattern. What is interesting to me is that in that case the beams which diffuse from the slits onto the screen are all in phase at the slits. What will happen if we use the first beam and another beam together to pass them through the slits? Will this cause a loss of intensity on the screen beacause two different beams are not supposed to be strictly in phase at the slits? Will in that case, every time we move one source of light towards the the slits, the intensity of light on the screen change?
 A: The result depends on one's ability to control the relative phase of the beams as well as the phase within the beams. The light emitted by a conventional light source is really not a beam, but a chaotic combination of waves going in all directions with random phases. In order to obtain an interference picture with such a light, every such wave has to interfere with itself, which excludes possibility of using different light sources.
The situation is different, if one uses lasers, which generate light much more homogeneous in terms of direction and phase. Still, contrary to the idealized textbook picture, there are many things happening in a real laser that diminish the coherence, and the result of the experiment may depend very much on the quality of the laser (e.g., laser diodes used in laser pointers are usually of very low quality, whereas gas lasers can produce extremely coherent beams).
Assuming that we have two lasers of high quality, so that we are not concerned with phase fluctuations within the beams itself, we still phase the problem of correlating the phases of the two beams. As the generation begins with a spontaneous (i.e., random) event, these phases are chosen randomly. This is not a problem by itself, but the phases will still fluctuate in time and space. However, if they remain stable over a long period of time and on the scale of the experimental setup, we could observe interference from two different sources.
A: Even single photons "interfere", but "interfere" is a misleading historical term to explain the DSE.  When a photon is emitted and absorbed its path is based on the geometrical properties of the source, slits, screen, and energy/wavelength of the light. Dark areas have no photons, bright areas all. Paths that are ideal are of length of multiples of the wavelength (Feynman), you could say where the EM field resonates is where the photons can travel.
Observed coherence and phase in the DSE are also a result of the setup geometry, the laser just makes it more obvious, not because the photons are in phase and more likely to "interfere" or cancel but more so because the photons are all similar (similar starting point and narrow frequency band) and the paths they choose are also more alike.  Even an incandescent source will produce the pattern, most visible when filtered to one color and sent thru an additional pinhole. The setup only accepts photons paths that fit the geometry.
So by adding an additional laser source nothing really changes, the photons choose their paths independently.
