Angular Separation of Stars: Min Resolved w/ Diffraction Effects

AI Thread Summary
The discussion focuses on calculating the minimum angular separation of stars that can be resolved by the human eye, specifically considering diffraction effects. The Rayleigh criterion formula, θ=(1.22*λ)/D, is used, with attempts made using different wavelengths (λ) and a pupil diameter (D) of 5.0 mm. Initial calculations yielded incorrect results, prompting confusion about whether a different wavelength should be used. Ultimately, the correct answer was revealed to be in arc minutes, specifically "0.46' of arc," which was not clearly indicated in the problem statement. This lack of clarity led to frustration, especially since other problems in the textbook used radians.
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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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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