If a mixture is separated, then the different components of the mixture will probably have different indexes of refraction, color, opacity, etc.

If you see your mixture as discontinuous, then it is separated. Most often it takes more than one separation method to separate a mixture. Here are some examples:

Chromatography separates based on polarity, charge.
Evaporation and Distillation (and Freezing) separates based on phases. One can use temperature and pressure to control this.
Decantation and Filtration (and Centrifugation) separate based on mass and size. For example, if you have a mixture of two liquids and they have different boiling points you can use distillation to separate them. After you have separated them you can check by refraction index or by MNR (magnetic nuclear resonance) spectrum to see how well you have separated them. Each substance has their own defined refraction index or MNR spectrum.