   Chapter 27, Problem 62PE

Chapter
Section
Textbook Problem

The limit to the eye's acuity is actually related to diffraction by the pupil.(a) What is the angle between two just-resolvable points of light for a 3.00-mm-diameter pupil, assuming an average wavelength of 550 nm?(b) Take your result to be the practical limit for the eye. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are 1.30 m apart?(c) What is the distance between two just-resolvable points held at an arm's length (0.800 m) from your eye?(d) How does your answer to (c) compare to details you normally observe in everyday circumstances?

To determine

(a)

What is the angle between two just-resolvable points of light for a 3.00-mm-diameter pupil, assuming an average wavelength of 550 nm?

Explanation

Given info:

λ=550nm=5.5×107mD=3mm=3×103m

Formula used:

Angle,

θ=1.22λD , λ is the wavelength and D is the diameter of the aperture, lens, mirror etc.

Calculation:

We have,

θ=1

To determine

(b)

What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are 1.30 m apart?

To determine

(c)

What is the distance between two just-resolvable points held at an arm's length (0.800 m) from your eye?

To determine

(d)

How does your answer to (c) compare to details you normally observe in everyday circumstances?

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