determine the wavelength of the offending laser light so that you can figure out which other researcher to ask to modify the aiming of his laser.

You are working in an optical research laboratory. One of your projects involves the use of a double slit through which you pass orange laser light of wavelength 590 nm. Unfortunately, because of budget cuts, there are a lot of researchers in the same room, with lots of equipment stuffed in the room, and, in particular, lots of laser beams flying around the room. One day, you find that a second laser beam of unknown origin and different color is entering your double slit along with your orange beam and you are seeing an interference pattern that is the sum of those due to the two beams. You notice that the combined pattern is pretty much a mess, but wait! The m 5 3 maximum of your orange laser beam pattern is pure; there is absolutely no mixture of the other color at that point. From this fact, you determine the wavelength of the offending laser light so that you can figure out which other researcher to ask to modify the aiming of his laser.