Public attention and fame, or the bright light from burning limestone that was used to light old theater stages.
From 'lime' (calcium oxide) plus 'light.' Before electric lights, theaters used limelight (also called calcium light) to illuminate actors on stage, making bright, focused beams possible.
Limelight was a real technology—burning calcium oxide created an incredibly bright white light, which is why it became the ultimate symbol for being 'on stage' and in public attention, and why we still use 'in the limelight' even though nobody burns limestone for light anymore.
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