  We present a detailed light curve analysis of RR Lyrae variables at multiple
wavelengths using Fourier decomposition method. The time-series data for RR
Lyrae variables in the Galactic bulge and the Magellanic Clouds are taken from
the Optical Gravitational Lensing Experiment survey while the infrared light
curves are compiled from the literature. We also analyse the multiband
theoretical light curves that are generated from the stellar pulsation models
of RR Lyrae stars for a wide range of metal-abundances. We find that the
theoretical light curve parameters with different metal abundances are
consistent with observed parameters in most period bins at both optical and
infrared wavelengths. The theoretical and observed Fourier amplitude parameters
decrease with increase in wavelength while the Fourier phase parameters
increase with wavelength at a given period. We use absolute magnitudes for a
subset of theoretical models that fit the observed optical RR Lyrae light
curves in the Large Magellanic Cloud to estimate a distance modulus,
$\mu_\textrm{LMC}=18.51\pm0.07$, independent of the metallicity. We also use
Fourier analysis to study the period-color and amplitude-color relations for RR
Lyrae stars in the Magellanic Clouds using optical data and find that the slope
of period-color relation at minimum light is very shallow or flat and becomes
increasingly significant at the maximum light for RRab stars. We also find that
the metallicity dependence of the period-color relations increases as we go
from minimum to maximum light, suggesting that the mean light results are
indeed an average of the various pulsational phases. We summarize that the
average variation in these relations is consistent between theory and
observations and supports the theory of the interaction of the stellar
photosphere and the hydrogen ionization front.
