Final answer:
No, two independent light sources such as car headlights would not produce the same interference pattern as observed in Young's double slit experiment because those light sources are not coherent, and coherence is necessary for a stable interference pattern.
Step-by-step explanation:
In Young's double slit experiment, a single light beam is split into two coherent sources, which then produce an interference pattern due to the superposition of the wavefronts from both slits. For two independent sources of light, such as the headlights of a distant car, the interference pattern would not be observed. This is because the light beams from the two headlights are not coherent; they do not have a constant phase relationship as they are emitted independently. Coherence is essential to form a stable interference pattern, where bright and dark fringes are predictable and repeatable.
The interference pattern observed in the Young's experiment is due to the constructive and destructive interference that happens when waves are in phase (constructive) or out of phase (destructive). Independent light sources, such as car headlights, emit waves that randomly fluctuate in phase and thus cannot produce the systematic pattern of light and dark bands that are characteristic of interference.