How does Stevens' Power law describe the relationship between intensity and sensation?

Stevens' Power Law addresses the relationship between the magnitude of a stimulus and the perceived intensity of that stimulus. Specifically, it suggests that the perceived intensity (or sensation) is related to the physical intensity of the stimulus raised to a power. This means that the relationship is not linear; instead, it can be described as exponential, depending on the type of sensation being measured.

For instance, when a stimulus's physical intensity is increased, the perceived intensity does not increase at the same rate. Instead, the increase in perceived intensity is proportional to the stimulus intensity raised to a specific exponent. This results in a curved relationship, which is indicative of an exponential scale rather than a straightforward linear relationship.

The power law implies that as the stimulus intensity increases, the perceived intensity increases, but not in a straight-line manner—hence, the sensation grows at a rate that depends on the original strength of the stimulus. This concept is fundamental in psychophysics, where understanding how humans perceive changes in stimuli is crucial.