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

Answer:

time is 5.973826 sec

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