Which error is characterized by varying densities on radiographs?

The characteristic of varying densities on radiographs is associated with quantum mottle, which refers to the grainy appearance on images caused by the statistical nature of photon detection. When x-rays or photons expose the imaging receptor, they do so in a random manner, leading to inconsistent density across the radiographic image. This phenomenon is more pronounced in images that utilize lower radiation doses, making it easier to visualize the variations in density.

In contrast, other options describe different types of radiographic errors. Motion blur results from movement during the exposure, leading to a loss of sharpness rather than density variations. Geometric distortion involves the misrepresentation of the size or shape of structures on the image, which does not primarily affect density. Film fog, caused by unwanted exposure or contamination, generally results in a uniformly increased background density rather than varying densities throughout the image. Therefore, quantum mottle is the most accurate choice when it comes to identifying the error linked to varying densities on radiographs.