Final answer:
Incandescent bulbs dim over time due to the increased resistance of the thinning tungsten filament, which causes less electrical power to be converted into light and the bulb to emit less light just before burning out.
Step-by-step explanation:
Incandescent lightbulbs grow dim late in their lives mainly because of increased resistance in the filament. As the tungsten filament is used, it gradually thins and evaporates, which increases its resistance.
The higher resistance means less current flows through it for a given voltage, according to Ohm's Law (V=IR). Additionally, as the filament gets thinner, its cross-sectional area decreases, causing its resistance to increase further. Increased resistance results in less electrical power being converted into light and more into heat, as per the power formulas P = V²/R and P = I²R. This heat does not contribute to luminosity but leads the filament towards failure, often observed as dimming particularly just before the filament breaks.