# How do we know if a solution of a chiral compound is optically active?

How else but by experiment? You need (i) to find a chiral carbon, i.e. $C {R}_{1} {R}_{2} {R}_{3} {R}_{4}$; this stereoisomer must (ii) be present in quantity.
If there is a $50 : 50$ mix of stereoisomers, then a solution of this mixture will NOT rotate plane-polarized light. A solution of the 1 stereoisomer, will rotate plane-polarized light.