In the model estimate for Hecht's experiment

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

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

Problem

In the model estimate for Hecht's experiment,

500

rods are pooled over an integration time of

0.1\,\mathrm{s}

, each with a thermal dark-event rate of

0.01\,\mathrm{s^{-1}}

, giving a pool mean of

m = 0.5

dark events and a false-alarm probability at threshold

3

of about

1.4\%

. Predict what happens if the flash detector instead integrates over

0.2\,\mathrm{s}

(twice as long), with the same

500

rods and the same dark rate per rod. ((a)) Compute the new pool mean

m

of dark events. ((b)) Compute the new false-alarm probability of getting

3

or more dark events by chance, using the Poisson distribution. ((c)) State in words why doubling the integration time is not simply good for sensitivity.

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