How does geometric penumbra (penumbra due to source size) vary with source-to-surface distance (SSD)?
See figure (GP = geometric penumbra). The penumbra is the distance between the rays arising from the center of the source and the rays arising from the edges of the source. As one moves farther from the collimators (i.e. increasing the SSD), that distance becomes larger, thereby increasing the geometric penumbra.