The pupil of an eagle\'s eye has a diameter of 6.0 mm. Two field mice are separa

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 176 m, the eagle sees them as one unresolved object and dives toward them at a speed of 17 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?

I got 88m for the distance at which the eagle sees the mice as separate objects, but am not sure on how to get the time...

Thank you!

Explanation / Answer

resolving power with perfect optics is (resolving angle) = (wavelength)/(diameter of lens)

So in your case the resolving angle would be 5.5 X 10-7/6X10-3 = 1X10-4

The initial angle when the eagle starts is 1X10-2/176 = 5 X 10-5

And it is below the resolving power of the eagle. However it is half the resolving power so the eagle will be able to resolve the mice at 1/2 the distance of 176 or about 88meters

therefore time T=Distance/Speed

T=88/17m/s=5.17 sec

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