SET UP AND SOLVE Part (a): (Figure 1) shows the situation. We use ^Rayleigh = 1.
ID: 1487986 • Letter: S
Question
SET UP AND SOLVE Part (a): (Figure 1) shows the situation. We use ^Rayleigh = 1.22X/D with the diameter D = 2(radius) = 2(0.25cm) = 0.50cm = 5.0 x 10 3m The iris of the eye is a circular aperture that allows light to pass into the eye. (a) For an iris with radius 0.25 cm, and for visible light with a wavelength of 550 nm, what is the resolving angle, or limiting resolution, of the eye. based on Rayleigh's criterion? (b) In fact, the actual limiting resolution ofthe human eye is about four times poorer: 0rRS = 401. What is the farthest distance s from a tree that you could stand and resolve two birds sitting on a limb, separated transversely by a distance y = 11cm? Part (b): Using Bies = 40. we find that the actual limiting resolution ofthe human eye is To find the farthest distance s from the tree that you could stand and still resolve two birds separated by 11 cm, we use the small-angle approximation: REFLECT This result is a rather optimistic estimate ofthe resolving power ofthe human eye. Many other factors, including the illumination level and small defects of vision, also act to limit the actual resolution. Part A - Practice Problem: For a person whose vision has angular resolution ten times poorer that given by the Rayleigh criterion, what is the maximum distance at which the person can distinguish two birds sitting 11 cm apart on a tree limb? Express your answer to two significant figures and include appropriate units. 82 mExplanation / Answer
Angular resolution of person, = 10 * ray = 10 * (1.34 * 10-4) = 1.34 * 10-3 rad
Using small angle approximation,
= y/s
=> maximum distance for resolution, s = y/ = 11 / (1.34 * 10-3) = 8200 cm = 82 m
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.