“Retrospective” has to do with looking back, as is shown by the similarity of its middle syllable to words like “spectacles.” A retrospective exhibit looks back at the earlier work of an artist.
“Retroactive,” on the other hand, refers to actions, and is about making a current change applicable to the past, especially in law. Retroactive punishment is generally considered unjust. For instance, the city council can’t pass an ordinance retroactively punishing you for having sung off-key in the karaoke bar on Main Street last Saturday night.
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