Question

An astronaut is looking down on earth's surface from a space shuttle at an altitude of $400km$. Assuming that the astronaut's pupil diameter is $5mm$ and the wavelength of visible light is $500nm$, the astronaut will be able to resolve linear objects of the size about

• A. 0.5 m
• B. 5 m
• C. 50 m
• D. 500 m

Answer 1

Answer: (C)

The resolving power of the eye is given by
$R=1.22\frac{\lambda }{b}\times D$
where $\lambda$ is the wavelength of light, $b$ is the diameter of the eye lens and $D$ is the distance from the lens at which light is focused.
$D=400km=400000m,d=5mm=5\times 10^{-3}m$
$\lambda =500nm=500\times 10^{-9}m$
$\therefore R=1.22\times \frac{500\times 10^{-9}\times 4\times 10^5}{5\times 10^{-3}}=48.8\approx 50$