Final answer:
The interference equations are not valid with incandescent light through double slits because the light is neither monochromatic nor coherent, which are necessary conditions for clear interference patterns like those seen in Young's double-slit experiment.
Step-by-step explanation:
The two-source interference equations are not valid for light from an incandescent bulb passing through a screen with two narrow slits because such light is not monochromatic and does not consist of coherent sources. Incandescent bulbs emit light with a broad spectrum of wavelengths, and without being passed through one slit before the double slits, the light waves do not have a definite phase relationship, making them incoherent. This incoherence means that the individual light waves emitted by the bulb are out of phase with each other, such that they produce a jumble of overlapping wave peaks and troughs on the observation screen instead of a clear pattern of interference fringes.
For clear interference patterns to emerge, the light must be both monochromatic and coherent, as demonstrated in Young's double-slit experiment, where light is first passed through a single slit to render it somewhat coherent before it encounters the double slits.