The Weber–Fechner law says that the relationship between Gustav Fechner was a student of Ernst Weber and named the law after his mentor, in recognition of the experimental work done by Weber that led to the formulation of the law. It is wonderful to see a student behaving with such respect to their teacher.

Just saying.

stimulus and perception is logarithmic. Thus, if p denotes the output of some perception system (vision, say, or hearing) and S denotes the stimulus (light, say, or sound), then p(S) = k ln 

S S0



, for some constants k and S0. The derivative of p is a useful measure of how sensitive the detection system is.

a. Calculate p 0

(S). What is limS→0 p 0

(S)? What does this tell us about the sensitivity of a detection system as S gets small?

b. What is limS→∞ p 0

(S)? What does this tell us about the sensitivity of a detection system as S gets large? Does this agree with your experience?