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 204 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?

Answer 1

Answer:6.74 s

Explanation:

Given

diameter$\left ( D\right )$=6 mm

d=0.01m

L=204 m

v=17 m/s

$\lambda =550 nm$

from rayleigh's critterion for resolution

$\theta =\frac{1.22\lambda }{D}=\frac{d}{L'}$

$L'=\frac{D\cdot d}{1.22\lambda }$

$L'=89.418 m$

$t=\frac{L-L'}{v}$

$t=\frac{114.581}{17}=6.74 s$