Weber–Fechner law

In psychophysics, the Weber–Fechner law combines two different laws of human perception, which both describe ways the resolution of perception diminishes for stimuli of greater magnitude. Ernst Heinrich Weber (1795–1878) was one of the first people to approach the study of the human response to a physical stimulus in a quantitative fashion. Weber's law states that the just-noticeable difference between two stimuli is proportional to the magnitude of the stimuli, (and the subject's sensitivity), i.e. if you sense a change in weight of 0.5 lbs on a 5 pound dumbbell, you ought to feel the extra pound added to a ten pound dumbbell. Gustav Theodor Fechner (1801–1887), a scholar of Weber, later used Weber's findings to construct a psychophysical scale in which he described the relationship between the physical magnitude of a stimulus and its (subjectively) perceived intensity. Fechner's law (better referred to as Fechner's scale) states that subjective sensation is proportional to the logarithm of the stimulus intensity. Fechner scaling has been mathematically formalized. In fact, human perceptions of sight and sound work as follows: Perceived loudness/brightness is proportional to log of actual intensity measured with an accurate nonhuman instrument.