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 186 m, the eagle sees them as one unresolved object and dives toward them at a speed of 20 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?

To determine how much time passes until the eagle sees the mice as separate objects, we need to consider the resolving power of the eagle's eye and the time it takes for the light to reach the eye.

1. Resolving Power of the Eye:
The resolving power of a telescope or an eye is determined by the diameter of its pupil. The formula to calculate the resolving power is:

θ = 1.22 * λ/D

where:
θ is the minimum resolving angle,
λ is the wavelength of light used, and
D is the diameter of the pupil.

In this case, the diameter of the eagle's eye pupil is given as 6.0 mm, which is equivalent to 0.006 m. The wavelength of light detected by the eye is 550 nm, which is equivalent to 550 * 10^-9 m.

Plugging these values into the formula, we can calculate the minimum resolving angle (θ) of the eagle's eye.

θ = 1.22 * (550 * 10^-9) / 0.006

2. Time for Light to Reach the Eye:
Since the eagle is diving towards the mice, we need to consider the time it takes for the light to reach the eagle's eye. This can be calculated using the distance traveled by the eagle and its speed.

Time = Distance / Speed

In this case, the distance is given as 186 m and the eagle's diving speed is 20 m/s.

Plugging in these values, we can calculate the time it takes for the light to reach the eagle's eye.

Time = 186 / 20

3. Total Time:
The total time until the eagle sees the mice as separate objects can be calculated by adding the time for the light to reach the eye and the resolving time of the eye.

Total Time = Time for Light to Reach the Eye + Resolving Time

Now, we can calculate the total time by adding the two values calculated in steps 2 and 3.

Total Time = Time + Resolving Time

Finally, plug in the values and compute the result to find out how much time passes until the eagle sees the mice as separate objects.