Can you see urine in a swimming pool?

no not really.

it will disolve in to the pools chemicals and that's what makes it invisable.

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The concentration from one or two little accidents is too small to see, but it is urine, perspiration etc that is responsible for sore eyes etc.

In chlorine-treated pools at least, they react with the disinfectant to produce unpleasant irritants and release chlorine. The chlorite itself does not cause irritation when used in the correct dilution (2 - 4ppm).