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 185 m, the eagle sees them as one unresolved object and dives toward them at a speed of 16 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

time is 5.973826 sec

Step-by-step explanation:

Given data

diameter D = 6.0 mm 6×
`10^(-3)` m

separated d = 0.010 m

distance (dis) 185 m

speed s = 16 m/s

wavelength = 550 nm = 550
`10^(-9)` m

to find out

How much time passes

solution

we know that for resolution we use Rayleigh's Criterion i.e

θ = 1.22 wavelength / diameter = separated / distance 1

we calculate distance 1 by put value wavelength, diameter and separated

distance 1 = diameter × separated / 1.22 wavelength

distance 1 = 6×
`10^(-3)` × 0.010 / 1.22 × 550 ×
`10^(-9)`

distance 1 = 89.418778

so time will be i.e = distance (dis) - distance 1 / speed

time = ( 185 - 89.418778) / 16

time = 5.973826 sec

time is 5.973826 sec