Solving Grating Resolution Homework for Skyscraper Distance

In summary, the conversation discusses the resolution of two lights on a skyscraper from a specific distance. It mentions the diameter of the pupils, the wavelengths of the blue and red lights, and the equations used to determine the minimum angular separation that can be resolved. The distance to the skyscraper is approximately 10km, but the process for determining this distance is not mentioned.
  • #1
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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  • #2
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".
 

What is grating resolution and how does it relate to skyscraper distance?

Grating resolution is the ability to distinguish between closely spaced lines or features. In the context of skyscraper distance, it refers to the ability to accurately measure the distance between two skyscrapers.

Why is it important to solve for grating resolution in skyscraper distance?

Accurately measuring the distance between skyscrapers is important for a variety of reasons, such as ensuring structural stability and safety, determining property values, and planning for construction and development.

What factors affect the grating resolution for skyscraper distance?

The factors that affect grating resolution for skyscraper distance include the quality and precision of the measuring instruments, atmospheric conditions, and the distance between the observer and the skyscrapers.

What methods are commonly used to solve for grating resolution in skyscraper distance?

Some common methods include using laser rangefinders, optical instruments, and mathematical calculations based on trigonometry and geometry.

Can grating resolution be improved or enhanced for more accurate measurements?

Yes, there are various techniques and technologies that can be used to improve grating resolution, such as using higher resolution instruments, correcting for atmospheric conditions, and using multiple measurements and calculations to reduce error.

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