Just noticeable difference

Another key psychophysical concept is the just noticeable difference (JND). This is the amount that the stimulus needs to be changed so that subjects would perceive it to have changed in at least 50 percent of trials. For a large change, all or nearly all subjects would report a change. If the change is too small, then none or nearly none of the subjects would notice. The experimental challenge is to vary the amount of change until the chance of someone reporting a change is 50 percent.

Consider the JND for a stimulus with varying magnitude, such as brightness. How does the JND itself vary as the magnitude varies? This relationship is captured by Weber's law:

$${\Delta m \over m} = c,$$ (2.2)

in which $\Delta m$ is the JND, $m$ is the magnitude of the stimulus, and $c$ is a constant.