Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 120 cm apart. If the resolution of your eye is limited only by diffraction, at what distance are the two headlights marginally resolved? Assume the light’s wavelength in air is 600 nm andthe index of refraction inside the eye is 1.33. (Your eye is not really good enough to resolve headlights at this distance, due to aberrations in the lens.)

Consider the following. (a) Find the angle ? locating the first minimum in the Fraunhofer diffraction pattern of a single slit of width 0.182 mm, using light of wavelength 581 nm.(b) Find the angle locating the second minimum.

(a) How far from some grains of red sand must you be so that you are just at the limit of resolving the grains if your pupil diameter is 3mm, the grains are spherical with radius 50μm, and the light from the gains has wavelength 650nm? (b) If the grains were blue and the light from them had wavelength 400nm instead, would the answer to (a) be larger or smaller? (c) Now let's say you are a superhero and you had x-ray vision, so you could see light that had a wavelength of 0.1nm instead. Now how far could you be from the gains of sand to just be at the limit to distinguish one grain of sand from another? (with the same pupil diameter). (assume you're on the beach and there's plenty of light from many frequencies bouncing off the sand, and when you turn on your x-ray vision you aren't bothered by all the other frequencies around).

Suppose that two points are separated by 2.0 cm. If they are viewed by an eye with a pupil opening of 5.0 mm, what distance from the viewer puts them at the Rayleigh limit of resolution? Assume a light wavelength of 500 nm.

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The limit to the eye's acuity is actually related to diffraction by the pupil. What is the angle between two just-resolvable points of light for a 2.75 mm diameter pupil, assuming the average wavelength of 539 nm? angle between two points of light: Take the result to be the practical limit for the eye. What is the greatest possible distance a car can be from a person if he or she can resolve its two headlights, given they are 1.40 m apart? greatest distance at which headlights can be distinguished: m What is the distance between two just-resolvable points held at an arm's length (0.900 m) from a person's eye? distance between two points 0.900 m from a person's eye: m

An amateur astronomer wants to build a telescope with a diffraction limit that will allow him to see if there are people on the moons of Jupiter.  (a) What diameter mirror is needed to be able to see 1.00 m detail on a Jovian Moon at a distance of 7.50×108 km from Earth? The wavelength of light averages 600 nm.  (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?