Explanation Introduction: The resolution limit for the pupil of an eye is defined by the Rayleigh’s criteria, α r e s = 1.22 λ D Here, D is the diameter of the pupil lens through which light enters, λ is the wavelength of light and α r e s is the resolution limit measured in radian. The distance between the two objects considering their angular separation is, d = α r e s l Here, α r e s is the small angular separation between the two objects and l is the distance between the objects and the eyes. Explanation: Assume: 1. The Rayleigh’s criteria uses small angle approximation, that is sin α r e s ≈ α r e s . 2. Assuming the wavelength of light to be 550 nm which is dominant as a visible wavelength 3. Assuming the diameter of the pupil is 0.5 cm and the distance between the car’s headlight is 1.5 m. Write the expression for the resolution limit of the eyes, α r e s = 1.22 λ D Substitute 500 nm for λ and 0.5 cm for D , α r e s = 1.22 ( 500 nm ) 0.5 cm = 1.22 ( 500 nm ( 1 m 10 9 nm ) ) 0

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Chapter 24, Problem 69GP

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The maximum distance between a car and a person within which the person’s eyes can resolve the two headlights, along with the assumptions made.

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Chapter 24, Problem 68GP

Chapter 24, Problem 70GP

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The maximum distance between a car and a person within which the person’s eyes can resolve the two headlights, along with the assumptions made.

Solution Summary: The author explains the Rayleigh's criteria for determining the resolution limit for the pupil of an eye and the distance between the two objects.

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The maximum distance between a car and a person within which the person’s eyes can resolve the two headlights, along with the assumptions made.

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Chapter 24 Solutions