Angular Separation of Stars: Min Resolved w/ Diffraction Effects

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Homework Help Overview

The discussion revolves around determining the minimum angular separation that the human eye can resolve when observing two stars, specifically considering diffraction effects. The problem is situated within the context of optics and involves the Rayleigh criterion for resolution.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of the Rayleigh criterion and explore how varying parameters such as wavelength and pupil diameter might affect the resolution. There is uncertainty regarding the correct units for the answer, with some participants questioning whether the result should be in radians or arcminutes.

Discussion Status

The conversation reflects a mix of attempts to apply the relevant equation and clarify the problem's requirements. Some participants have offered insights into minimizing the angular separation, while others express confusion over the expected format of the answer. There is no explicit consensus on the correct approach or solution, but participants are actively engaging with the problem.

Contextual Notes

Participants note that the problem's phrasing may have led to misunderstandings, particularly regarding the expected units for the answer. There is also mention of a deadline, which adds pressure to resolve the issue quickly.

grouper
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Homework Statement



What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects?

Homework Equations



θ=(1.22*λ)/D

The Attempt at a Solution



I tried estimating with λ=550 nm and D=5.0 mm (pupil diameter) which appeared in another problem about viewing stars and got 1.34e-4 rad, but this was incorrect. Our book states the best eye resolution is around 5e-4 rad so I tried that as well, but it wasn't correct either. This problem must want something more concrete than an estimation but I'm not sure where to go with it.
 
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They're asking for a minimum here. According to rayleigh equation which you've written there, what criterion would minimize the angle theta?
 
I suppose either a smaller wavelength or a larger diameter; do you think I should be using a different λ for my estimation? If I use λ=400 nm (keeping D=5.0 mm), that yields θ=9.76e-5 rad, but that's not correct either. I got the 5.0 mm diameter from another problem, so I'm not sure adjusting the diameter will get a correct answer either.
 
I figured out the problem; they were asking for arcs. Wasn't indicated anywhere but I eventually gave up on this problem since it's due tonight and when it showed the correct answer it read "0.46' of arc". Would've been nice if they said that in the problem, especially considering all the other problems in our book deal in radians. Oh well.
 

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