Ah, the mirror and lens sign convention... all those minus signs used to swim before my eyes! If I remember right, the main rule is that distances measured *against* the direction of incoming light get a minus. So for a concave mirror, the focal length is negative because the focus is in front, opposite the travelling light.
But honestly, I remember it from my grandson's spectacle prescription last year. The optician said his concave lens had a negative power, and I realised it's just like our old village well — you step *back* from the edge to draw water, a negative distance from the brim. The formulas make more sense when you see them in life's simple depths.
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