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Math · Calculus
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Light enters the eye through the pupil and strikes the retina, where photoreceptor cells sense light and color. W. Stanley Stiles and B.H. Crawford studied the phenomenon in which measured brightness decreases as light enters farther from the center of the pupil. See the figure A light beam A that enters through the center of the pupil measures brighter than a beam B entering near the edge of the pupil. They detailed their findings of this phenomenon, known as the Stiles-Crawford effect of the first kind, in an important paper published in 1933. In particular, they observed that the amount of luminance sensed was not proportional to the area of the pupil as they expected. The fraction P of the luminance entering a pupil of radius r mm that is sensed at the retina can be described by 1 10 pr2 In(10) where p is an experimentally determined constant, typically about 0.05.t (a) What is the percentage of luminance P sensed by a pupil of radius 3 mm? Use p 0.05. Round your answer to one decimal place P 62.3 (b) Compute the percentage of luminance P sensed by a pupil of radius 1 mm. Round your answer to one decimal place.) P 90 Does it make sense that it is larger than the answer to part (a)? This makes sense since Stiles and Crawford found that light entering closer to the center of the pupil measures brighter than ght entering farther away from the pupils center. (c) Compute lim P. 100 Is the result what you would expect? Is this result physically possible? We expect this result since all the light entering at the center of the pup Wal be sensed at the retinaHelp with L'hopital's rule and limits. I have found everything but "B. Compute the percentage of luminance P sensed by a pupil of radius 1mm."

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