Solving Grating Resolution Homework for Skyscraper Distance

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SUMMARY

The discussion focuses on calculating the distance from a skyscraper based on the resolving power of the human eye, specifically in relation to two antennae emitting blue and red light. Using the formula θ=1.22λ/D, where λ represents the wavelength of light and D the diameter of the pupil, participants determined that the distance to the skyscraper is approximately 10 kilometers. The resolution capability is influenced by the wavelengths of blue (475 nm) and red (650 nm) light, with the ability to resolve blue lights but not red ones due to diffraction limits.

PREREQUISITES
  • Understanding of diffraction and resolving power in optics
  • Familiarity with the formula θ=1.22λ/D for angular resolution
  • Knowledge of light wavelengths, specifically in the visible spectrum
  • Basic principles of human vision and pupil diameter effects
NEXT STEPS
  • Study the principles of diffraction and its impact on optical resolution
  • Learn about the application of the Rayleigh criterion in resolving power
  • Explore the effects of different wavelengths on visibility and resolution
  • Investigate advanced optical systems and their resolving capabilities
USEFUL FOR

Students in physics or optics courses, educators teaching about light and vision, and anyone interested in the practical applications of resolving power in real-world scenarios.

Gee Wiz
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Homework Statement


Considering larger objects, a skyscraper has two tall antennae separated by 3 meters. Each antenna has one blue and one red light. You can resolve the two blue lights but not the red ones.

Assume that your pupils have a diameter = 2 mm at night, and that blue light's wavelength is 475 nm, while red light's wavelength is 650 nm.
Approximately how far are you from the skyscraper? (Also assume that you have 'perfect vision' limited only by diffraction.)

Physics114HWB21_3S.gif



Homework Equations



θ=1.22λ/D

Δλ/λ=1/(mN)

The Attempt at a Solution



I know the answer is 10km, but I don't know how to get that. I was trying to find a way to determine the resolution requirement, or something like that.
 
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There is a minimum angular separation that you can resolve two objects - it depends on the wavelength of the light and the diameter of the aperture. You should have some notes on this under "resolving power".
 

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