4/6/2014 Master Ithttp://www.webassign.net/v4cgi/questions/tutorial_popup.tpl 1/2Master ItThe Impressionist painter Georges Seurat created paintings with an enormous number of dots of purepigment, each of which was approximately 2.00 mm in diameter. The idea was to have colors such as redand green next to each other to form a scintillating canvas, such as in his masterpiece, A Sunday Afternoonon the Island of La Grande Jatte (figure below). Assume λ = 565 nm and a pupil diameter of 4.60 mm.Beyond what distance would a viewer be unable to discern individual dots on the canvas?Part 1 of 3 ConceptualizeThe farther we are from this painting, the less we can distinguish the individual dots of color. We estimatethat at a distance of several meters we will not be able to see the individual dots.Part 2 of 3 CategorizeThe resolving power of human vision is limited by the coarseness of the light sensors on the retina. We willuse Rayleigh's criterion to determine the distance at which the dots will be seen to merge.Part 3 of 3 AnalyzeWe assume that the dots in the painting are just touching and do not overlap so that the distance betweentheir centers is 2.00 mm. By Rayleigh's criterion, two dots separated center to center by a distance d wouldbe seen to overlap whenwhere D is the pupil diameter, L is the distance of observation, and λ is the wavelength of the light. Solvingfor L from the equation above, we obtain the following.θmin = = (1.22) ,dLλDL = = = 13.3 mDd(1.22)λ 4.6 × 10−3 m 2.00 × 10−3 m1.22 565 × 10−9 m4/6/2014 Master Ithttp://www.webassign.net/v4cgi/questions/tutorial_popup.tpl
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