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HOME >HOMEWORK #1

Homework #1: Assigned 6/20/01 Due 6/27/01 start of class

Reading: Aidley p 264-286. KSJ p 507-516

0. Take a look at the course web site if you have not already done so at http://courses.washington.edu/biophys/ and read over the handouts passed out today. Also, sign up for the class mailing list. I will start sending out messages to the list as early as tomorrow (6/21/01) so please sign up today if you can. You are responsible for any messages you miss if you fail to sign up.

1. (very easy) Imagine that I show you two flashes of slightly different intensity. The first flash, on average, causes 100 more photons to be emitted than the second. Explain why it may be physically impossible to determine which flash was brighter if each flash is presented only once.

2. You have a light source that produces flashes of an average intensity of 100 photons/flash. You shine this light source into your eye such that the flash illuminates 250 rods. You can see this flash 60% of the times that the flash is presented. You hypothesize that in order to see the flash, at least one rod must absorb 2 or more photons from the flash. Are your observations consistent with this hypothesis? What percentage of the photons must be absorbed by the rods? How does this number compare with the case that at least one rod must absorb 1 or more photons per flash in order to see the flash)?

3. Imagine the retina being illuminated by a steady light. The number of absorbed photons in any given time interval is Poisson distributed. Most of the time, we do not perceive steady light as flickering. Some experiments have shown that the dimmest transient light increment (a dim flash superimposed on the steady background light) that we can detect scales with the square root of the background (steady) light intensity. Does this result make sense? Why or why not?

4. Your retina is not perfect. There are noise sources due to spontaneous activity in the retina. This noise causes your retina to effectively always "see" a dim background light (that also follows Poisson statistics) even in complete darkness. Imagine we extend the experiment described in question 3 to very very dim background light intensities and get the result shown below. Do the results (shown below) make sense? Why or why not?

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