First slide

Diffraction

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 of about

Moderate

A

0.5 m
B

5 m
C

500 m
D

50 m

Solution

For wavelength $λ,$ d the diameter of eye lens and D the distance from the lens at which light is focused, the resolving power is given by
$RP = 1 .22 \frac{λ}{d} D$
Given, $D = 400 km = 400 \times 10^{3} m$
$d = 5 mm = 5 \times 10^{- 3} m$
$R = 1 .22 \times \frac{500 \times 10^{- 9} \times 4 \times 10^{5}}{5 \times 10^{- 3}} R = 50 m$

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