Final answer:
The halogen light has the hottest filament when compared to incandescent, fluorescent, and LED lights because its tungsten filament operates at a higher temperature due to the regeneration cycle enabled by the halogen gas within its quartz envelope.
Step-by-step explanation:
The light with the hottest filament among the options given is the halogen light. Halogen bulbs are a type of incandescent bulb and generally operate at higher temperatures than standard incandescent lights. They contain a tungsten filament similar to the standard incandescent, but the filament is enclosed in a much smaller quartz envelope. The halogen gas inside the envelope allows a regeneration cycle which permits the filament to operate at a higher temperature, resulting in a higher light output per unit of energy and giving them a longer lifespan.
By contrast, fluorescent lighting works by exciting mercury vapor that emits ultraviolet light, which then causes a phosphor coating on the inside of the bulb to glow. LED lights work by passing an electric current through a semiconductor, which emits light as it becomes excited. Neither of these methods involve heating a filament to a high temperature like incandescent or halogen bulbs do.
Incandescent bulbs do operate with heated filaments, but typically at lower temperatures compared to halogen bulbs. This is why halogen light bulbs can reach higher temperatures and thus have the hottest filament among the options provided.