The finding that the size of a just noticeable difference (JND) is a constant fraction of the intensity of the stimulus is known as Weber's Law. This principle, first observed by Ernst Heinrich Weber, states that the smallest change in a stimulus that can be detected is directly proportional to the intensity of the original stimulus. Mathematically, it is expressed as:
ΔI=k×I\Delta I=k\times IΔI=k×I
where ΔI\Delta IΔI is the just noticeable difference, III is the original stimulus intensity, and kkk is a constant fraction known as the Weber fraction. This means that as the stimulus intensity increases, the amount of change needed to notice a difference also increases in a consistent ratio. For example, if a light of 100 units requires a 10-unit change to be noticed (a ratio of 0.1), then a light of 1000 units would require a 100-unit change to be noticed. Weber's Law applies across different senses including brightness, weight, loudness, and temperature, with the constant kkk varying depending on the sensory modality. This law helps explain why it is harder to detect changes in more intense stimuli compared to less intense ones. In summary, the size of the just noticeable difference is a constant proportion of the original stimulus intensity, reflecting how our sensory systems perceive changes relative to stimulus magnitude.
