Final answer:
The limit to the eye's acuity is related to diffraction by the pupil. The angle between two just-resolvable points for a 3.00-mm-diameter pupil is 0.225 degrees. The distances between two resolvable points of light at different situations are also discussed.
Step-by-step explanation:
The limit to the eye's acuity is related to diffraction by the pupil, which affects the resolution of the eye. When determining the resolution limit, a circular aperture is considered, and the first minimum in the diffraction pattern occurs at an angle of 0 = 1.22λ/D, where λ is the average wavelength and D is the diameter of the pupil.
(a) For a 3.00-mm-diameter pupil and an average wavelength of 550 nm, the angle between two just-resolvable points of light is 0 = 1.22 * (550 nm) / 3.00 mm = 0.225 degrees.
(b) Taking the result from (a) as the practical limit, the greatest possible distance a car can be from you for you to resolve its two headlights, given they are 1.30 m apart, is determined by using the formula: distance = 2 * (1.30 m) * tan(0.225 degrees) = 0.0635 m.
(c) The distance between two just-resolvable points held at an arm's length (0.800 m) from your eye can be calculated using the formula: distance = 2 * (0.800 m) * tan(0.225 degrees) = 0.0427 m.
(d) The distance obtained in (c) is much smaller than the details normally observed in everyday circumstances, meaning that under normal conditions, our eyes can distinguish much smaller details than what is just-resolvable at arm's length.