How Is the Angular Width of a Central Diffraction Maximum Calculated?

AI Thread Summary
The discussion revolves around calculating the angular width of the central diffraction maximum for a circular aperture using the formula sinθ = 1.22(λ/d), where λ is the wavelength of the laser light and d is the diameter of the aperture. The user initially struggles with the calculation after converting the wavelength from nanometers to millimeters and applying the formula. After some confusion, the user realizes the correct answer shortly after posting and thanks the community for their assistance. The conversation highlights the importance of careful unit conversion and formula application in physics problems. Ultimately, the user successfully resolves the issue independently.
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Homework Statement



A beam of yellow laser light (580 nm) passes through a circular aperture of diameter 4 mm. What is the angular width of the central diffraction maximum formed on a screen? (Define the angular width as the full angle from one minimum of the central diffraction maximum to the diametrically opposite minimum.)


Homework Equations



sinθ=1.22(λ/d)

θ = angle to first minimum
λ = wavelength
d = diameter of aperture

The Attempt at a Solution



This problem seems to be fairly straightforward, but I'm not coming up with the correct answer. Convert λ to mm to get .00058, divide by 4, and then multiply by 1.22. This value is equal to sinθ, so simply take sin-1 of that number to get θ. Computer does not like this answer. Help, anyone? Thanks in advance!
 
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LOL. Disregard. Realized correct answer moments after posting. Thanks anyways!
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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