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 object of the size of about .

Options

A. (a) `0.5m`
B. (b) `5m`
C. (c) `500m`
D. (d) `50m`

Answer

D

Explanation

For wavelength `lambda`, d the diameter of eye lens and D the distance from the lens at which light is focussed, the resolving power is given by
`RP=1.22lambda/dD`
Given, `D=400 km=400xx10^3m`
`d=5mm=5xx10^-3m`
`lambda=500nm=500xx10^-9m`
`:. R=1.22xx(500xx10^-9xx4xx10^5)/(5xx10^-3) R=50m`