Final answer:
The two-source interference equations don't work for light from an incandescent bulb through double slits because it is not monochromatic and lacks coherence, resulting in an unpredictable interference pattern rather than distinct bright and dark fringes.
Step-by-step explanation:
The two-source interference equations are tailored for scenarios where light from monochromatic and coherent sources is utilized. The reason light from an incandescent bulb would not produce accurate double-split interference patterns is because it is neither monochromatic nor coherent. Light from an incandescent bulb comprises multiple wavelengths and the wavefronts are not in phase, which results in random interference effects rather than a predictable pattern of bright and dark fringes. When Thomas Young conducted his famous double-slit experiment, he used sunlight passed through a single slit to create somewhat coherent light with an observable, though complex, interference pattern. To simplify and clarify the experiment's demonstration of wave behavior, monochromatic light sources that produce light waves with the same wavelength and a stable phase relationship are preferred.
For coherent waves, the equation d sin θ = mλ, where d is the separation between the slits, θ is the angle from the central axis, m is the order of the fringe, and λ is the wavelength of light, can predict the positions of the bright (constructive interference) and dark (destructive interference) fringes. However, this equation does not hold for incoherent sources like an incandescent bulb the slits are close together and the screen is at a distance comparable to or smaller than the separation between the light sources, a clear interference pattern may not form. Instead, the light spreads and overlaps without creating distinct fringes.