||To predict the light pollution of the night-time sky realistically over any location or measuring point on the ground presents quite a difficult calculation task. Light pollution of the local atmosphere is caused by stray light, light loss or reflection of artificially illuminated ground objects or surfaces such as streets, advertisement boards or building interiors. Thus it depends on the size, shape, spatial distribution, radiative pattern and spectral characteristics of many neighbouring light sources. The actual state of the atmospheric environment and the orography of the surrounding terrain are also relevant. All of these factors together influence the spectral sky radiance/luminance in a complex manner. Knowledge of the directional behaviour of light pollution is especially important for the correct interpretation of astronomical observations. From a mathematical point of view, the light noise or veil luminance of a specific sky element is given by a superposition of scattered light beams. Theoretical models that simulate light pollution typically take into account all ground-based light sources, thus imposing great requirements on CPU and MEM. As shown in this paper, a contribution of distant sources to the light pollution might be essential under specific conditions of low turbidity and/or Garstang-like radiative patterns. To evaluate the convergence of the theoretical model, numerical experiments are made for different light sources, spectral bands and atmospheric conditions. It is shown that in the worst case the integration limit is approximately 100 km, but it can be significantly shortened for light sources with cosine-like radiative patterns.