We discuss a variety of photometric indices assembled from the uvby Strömgren system. Our aim is to examine the pros and cons of the various indices to find the most suitable one(s) for studying the properties of multiple populations in the globular clusters (GCs) discovered by spectroscopy. We explore in particular the capabilities of indices like m1 and c y at different metallicities. We define a new index δ4 = (u-v)-(b-y) to separate first and second stellar generations in GCs of any metal abundance, since it keeps the sensitivity to multiple stellar populations over the full metallicity range and at the same time minimizes the sensitivity to photometric errors. We detect clear differences in the red giant branches of the GCs examined, such as skewness or bi/multimodality in color distribution. We connect the photometric information with the spectroscopic results on the O and Na abundances we obtained in our survey of GCs. Finally, we compute the effects of different chemical composition on the Strömgren filters and indices using synthetic spectra.