  We analyze the dispersion property of low-index thin lenses by using scalar
diffraction and finite difference time domain (FDTD) methods. We compare the
dispersion results obtained by using these methods with reported experimental
results, and the well-known analytical formula for focal length (f) of
diffractive lenses as a function of wavelength ({\lambda}),f({\lambda})=(f_0
{\lambda}_0)/{\lambda},where f_0 is the designed focal length for wavelength
{\lambda}_0. We show that when the analytical formula is applied to thin flat
lenses with low-refractive index, the results are accurate for small numerical
aperture (NA) up to 0.2. For larger NA, the error between the analytical
approximation and the FDTD analysis remains around 8% over a wide range of NA.
