A cone photoreceptor obeys Weber's law, (a Weber fraction of )

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body · Bioelectricity, the senses and the physics of the body

Forces, Machines and Signals, Ch Vision and photoreception: counting photons

Problem

A cone photoreceptor obeys Weber's law,

\Delta I / I \approx 0.02

(a Weber fraction of

2\%

), over its working range of about

2.5

decades of background intensity

I

, measured in arbitrary photometric units. Take the bottom of its range as

I_1 = 200

units. ((a)) Compute the smallest detectable increment

\Delta I

at the bottom of the range,

I_1 = 200

. ((b)) The top of the range is

I_2 = I_1\times10^{2.5}

. Compute

I_2

and the corresponding

\Delta I_2

. ((c)) By what factor does the detectable increment itself change from the bottom to the top of the range? ((d)) Explain, using Weber's law, why a fixed absolute threshold (a fixed

\Delta I

, not a fixed fraction) would fail to serve this whole range.

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