Question

The pupil of an eagle’s eye has a diameter of 6.0 mm. Two field mice are separated by 0.010 m. From a distance of 201 m, the eagle sees them as one unresolved object and dives toward them at a speed of 18 m/s. Assume that the eagle’s eye detects light that has a wavelength of 550 nm in vacuum. How much time passes until the eagle sees the mice as separate objects?

Answer #1

The pupil of an eagle’s eye has a diameter of 6.0 mm. Two field
mice are separated by 0.010 m. From a distance of 176 m, the eagle
sees them as one unresolved object and dives toward them at a speed
of 21 m/s. Assume that the eagle’s eye detects light that has a
wavelength of 550 nm in vacuum. How much time passes until the
eagle sees the mice as separate objects?

(a) Take the diameter of the pupil of Cyclops’s eye to be 6.5
mm, and calculate the resolution angle Theta = 1.22 Lamda/ D (rad)
for light of wavelength 550 nm. For two point-objects to be
resolvable with light of this wavelength, how far apart must they
be (i) at distance 100 m? (ii) on the moon, 400,000 km away? (b)
How far apart must they be on the moon to be resolvable with a
telescope mirror of diameter 6.5...

Calculate the limiting angle of resolution for the eye, assuming
a pupil diameter of 1.75 mm, a wavelength of 520 nm in
air, and an index of refraction for the eye of 1.33.
____ rad
(b) What is the maximum distance from the eye at which two points
separated by 14.00 cm could be resolved?
____m

a) The Mount Palomar telescope has an objective mirror with a
508 cm diameter. Determine its angular limit of resolution at a
wavelength of 550 nm (in radiants and degrees). (Recall that you
can resolve two objects only if the maxima of their images are
separated by at least the radius of the first dark fringe of each
image’s Airy disk).
b) How far apart must two objects be on the surface of the Moon
if they are to be...

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