To produce full brilliance, the filament in an incandescent lamp needs to be heated to approximately what temperature?

The filament in an incandescent lamp needs to reach a temperature of around 5,000 degrees Fahrenheit to produce full brilliance. At this temperature, the filament emits visible light efficiently, primarily in the range of short wavelengths, which corresponds to a bright white light.

This temperature is ideal because it balances the heat and light output; if the filament were to be heated much more than this, it might produce excessive infrared radiation instead, which does not contribute to visible light and can lead to reduced efficiency and lifespan of the lamp. The other options present temperatures that either underperform in terms of light output or exceed the optimal operational range for incandescent filaments, thus resulting in diminished efficacy or rapid degradation of the filament materials.