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

Step-by-step 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 =(1.22\lambda )/(D)=(d)/(L')`

`L'=(D\cdot d)/(1.22\lambda )`

`L'=89.418 m`

`t=(L-L')/(v)`

`t=(114.581)/(17)=6.74 s`