# Resolving Power/Angle etc.

Hello all, I'm little stumped on this question. Have tried multiple times and can not find the right answer to it. Here it is:

1. Question

The pupil of an eagle's eye has a diameter of 5.93 mm. Two field mice are separated by 0.0124 m. From a distance of 186 m, the eagle sees them as one unresolved object and dives toward them at a speed of 18.1 m/s. Assume that the eagle's eye detects light that has a wavelength of 565 nm in a vacuum. How much time passes until the eagle sees the mice as separate objects?

3. The Attempt at a Solution

565e-9/5.93e-3 = 9.527824620573355e-5 or approx 1.00x 10^-4 which is the resolving angle
.0124/186 = 6.666666666666667e-5 which is approx 2/3 of resolving angle (this is angle when eagle starts)

if taking 2/3 of 186m I get 124.

124m / 18.1 m/s = 6.85s

cepheid
Staff Emeritus
Gold Member
Why don't you just solve for the distance at which the angular separation of the mice is equal to the resolution limit?

(0.0124 m)/(d) = (565 nm)/(5.93 mm)

Solve for d.

Your approach was fine, and equivalent, except that you introduced a huge rounding error by rounding that first angle up.

I actually had 7.19s as my first answer which is what you get when you solve for d. This answer is apparently wrong though..

cepheid
Staff Emeritus