Okay, so for the mirror and lens sign convention, we just have to remember the "New Cartesian Sign Convention" – basically, take the pole or optical centre as the origin, and light travels from left to right. The object distance 'u' is always negative. For a concave mirror or convex lens, 'f' is negative and positive respectively... that's where the minus signs start. Honestly, all these signs get jumbled when I'm sleepy.
My life says this because I *just* re-copied the table into my notebook last night, my father's shop ruler acting as a straightedge, while rain drummed on our tin roof. The real confusion isn't the rule, but applying it when my brain is fried from too much "Ray Optics.
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