Question

An astronaut is looking down on earth's surface from a space shuttle at an altitude of $400\, km$. Assuming that the astronaut's pupil diameter is $5 \,mm$ and the wavelength of visible light is $500\, nm$, 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)

50 m

Answer 2

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. $D = 400\, km = 400000 \,m, d = 5 \,mm = 5 \times 10^{-3}\, m$ $\lambda = 500 \,nm = 500 \times 10^{-9}\, m$ $\therefore R= 1.22\times\frac{500\times10^{-9}\times4\times10^{5}}{5\times10^{-3}}=48.8\approx50$