The “resolving power” of any optical system is limited by the wave-like property
ID: 1694900 • Letter: T
Question
The “resolving power” of any optical system is limited by the wave-like property of light–and photons–through diffraction or interference. This is often described by the “Rayleigh criterion” which states that the minimum angular separation dR for two objects to be resolved by an optical system having a circular aperture of diameter D using light of wavelength ? is dR = 1.22 ?/D. What is the minimum distance d between two points on the earth’s surface can be resolved by the GeoEye optical system discussed in the previous question at anominal wavelength of ? = 550 nm?(Refer this question as Previous question)
Often, sodium vapor lamps are used to illuminate large outdoor areas because they
mainly radiate at two nearly equal wavelengths, the sodium yellow “D” lines ? =589 nm. Suppose a 1 kW lamp is 50% efficient at producing photons at this wave-length. How many such photons are produced per second? Assuming the photons radiate isotropically from the lamb, how may photons enter the pupil of one of your eyes if you are standing 100 m from the lamp? Assume the pupil to have a radius of 1 mm.
Now suppose the“GeoEye-1” satellite, a supplier of images for Google-Earth, is
observing the area around the lamp at night. Assume the satellite collects all the
photons hitting a 1 m diameter circular aperture formed by its imaging system when
it is looking straight down from its orbital altitude of 681 km. How many photons
per second are collected from the lamp by GeoEye?
**Explain in details please**
Explanation / Answer
The minimum distanfe d between the two point on the earth's surfaced = (1.22 ?H)/D
Here ? = 550x 10^-9 m H = 681 x 10^3m D = 1.0 m d = (1.22 (550x 10^-9 m)(681 x 10^3m))/(1.0 m) = 0.456951 m
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