Suppose you are observing the interference pattern formed by a Michelson interferometer in a laboratory and a joking colleague holds a lit match in the light path of one arm of the interferometer. Will this have an effect on the interference pattern

In Michelson interferometer, two light waves from different directions are made to overlap so that fringes are formed on the screen due to interference. In it, two monochromatic and coherent light are made to overlap which have some path difference or phase difference. They form dark and bright fringes.

Now when a match stick is lit in the path of a wave, the fringes will disappear and an general illumination will be observed on the screen as the light from the lit match stick will not be coherent. Incoherent light can not form stable fringes.