A comb with closely-spaced teeth used for grooming fine or delicate hair, or for removing lice and nits.
From 'fine' (small, closely-spaced) plus 'comb,' a straightforward descriptive compound. The tool itself dates to ancient times, with the name reflecting its characteristic narrow tooth spacing.
A fine-tooth comb has been used literally and metaphorically for centuries—'go through with a fine-tooth comb' means thorough examination, showing how objects become metaphors when they're so useful everyone knows them.
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