Spatial distributions of the near-field and internal electromagnetic intensities have been calculated and experimentally observed for dielectric cylinders and spheres which are large relative to the incident wavelength. Two prominent features of the calculated results are the high intensity peaks which exist in both the internal and near fields of these objects, even for nonresonant conditions, and the well-defined shadow behind the objects. Such intensity distributions were confirmed by using the fluorescence from iodine vapor to image the near-field intensity distribution and the fluorescence from ethanol droplets impregnated with rhodamine 590 to image the internal-intensity distribution.