Weber Fechner’s Law Explained

The world around you provides many stimuli at a time but you do not respond to all stimuli, particularly those which are very low in intensity. Different types of sensations need the different intensity of stimuli for activation.

Gustav Theodor Fechner, the founder of psychophysics attempted to measure the just noticeable difference (j.n.d) with a view of achieving a higher goal that is, formulation of a law relating stimulus intensity to sensory magnitude. He believed that the sensation cannot be compared to physical stimuli but they can be easily compared to each other. A person can compare two of his sensation and judge whether the two are the same or different. Fechner believed that such a law could be built upon an empirical generalisation first proposed by E.H. Weber, a German physiologist, in the year 1834.

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Weber’s Law

Weber gave an observation that the size of the difference threshold is directly proportional to the intensity of a standard stimulus. This ratio is constant. The size of the difference threshold or the j.n.d is a constant ratio of the standard stimulus, which is often referred to as Weber Fraction. For example, suppose that you can just tell the difference between 100 and 104 grams then you will be able to just distinguish between 200 and 208 grams, 400 and 416 grams and so on. Fechner labelled it as the Weber’s law which is algebraically expressed as,

DI/I = C

Where DI is the increment is stimulus intensity. (i.e. the just noticeable difference), I is the stimulus intensity (the standard stimulus) and C is a constant.

Many studies were conducted in the past to see whether Weber’s law holds for all the sensory modalities. It was verified in most of the cases except for a few cases where the nervous system blended to notice relative differences rather than absolute ones. This law allows us to compare the sensitivities of different sensory modalities.

Suppose you want to know, whether the eye is more sensitive than the ear. This can be seen using Weber’s law. If Weber’s ratio is small, then the discriminative power of the sense modality is great and vice versa. This law helps us to understand the salient features of different sense modalities. It has been found out that, using this law, the humans are keen in discriminating brightness than loudness, and Weber’s fraction being 1/62 and 1/11 respectively.

Fechner’s Law

We have seen that Weber’s law postulates that the most intense the stimulus, the more the stimulus intensity needs to be increased before the person gets a change. Fechner, with several assumptions, generalised Weber’s findings which indicated a broader relationship between sensory and physical intensity.

Fechner’s law says that the strength of a sensation grows as the logarithm of stimulus intensity. The formula he gave is expressed as,

S = K log I

Where S is psychological magnitude. I is stimulus intensity and K is a constant.

Fechner’s law makes more sense than Weber’s law as our nervous system compress a huge range of sensation awareness into some manageable extent and this is what a logarithmic transformation does for us.