Question

What is the approximate size of the smallest object on the Earth that astronauts can resolve by eye when they are orbiting 250 km above the Earth? Assume λ = 500 nm and a pupil diameter of 5.00 mm

Answer 1

The equation find the smallet objects is

Where dmin is the size of the smallest object

(2)

is the limiting angle of resolution

is the wave length

D is the pupil diameter

= 500nm = 500* 10^-9

D = 5mm = 5*10^-3

= 1.22*((500*10^-9)/(5*10^-3))

= 1.22 * 10^-4 radian (3)

L = 250 km = 250*10³ m

apply (3) in (1)

tan(1.22 * 10^-4) = dmin/(250*10³)

dmin = (250*10³)*(tan(1.22 * 10^-4))

dmin = 30.5 m

that is that astraunut can see a object with minimum 30.5 m diameter from 250 km above earth

note that taken in radian OR other wise it converted to degree

we got = .00699⁰