Problem 24.39 Once dark adapted, the pupil of your eye is approximately 7 mm in

Question

Problem 24.39

Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 120 cm apart.

Part A

If the lens of your eye is diffraction limited, at what distance are the two headlights marginally resolved? Assume a wavelength of 595 nm and that the index of refraction inside the eye is 1.33. (Your eye is not really good enough to resolve headlights at this distance, due both to aberrations in the lens and to the size of the receptors in your retina, but it comes reasonably close.)

Express your answer to two significant figures and include the appropriate units.

Problem 24.39

Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 120 cm apart.

Part A

If the lens of your eye is diffraction limited, at what distance are the two headlights marginally resolved? Assume a wavelength of 595 nm and that the index of refraction inside the eye is 1.33. (Your eye is not really good enough to resolve headlights at this distance, due both to aberrations in the lens and to the size of the receptors in your retina, but it comes reasonably close.)

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

use the raylegih Criterion

R = 1.22 L/d

where L is wavelength

d is slit width

R = 1.22 * 595 e -9 /7 e-3

R = 0.1037 mm

angular separation theta = D/L

where L is required distance

so

L = Dd/1.22 l

L = 1.2 * 7 e -3/(1.22 * 595 e -9)

L = 11.57 Km

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