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

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SUMMARY

The angular width of the central diffraction maximum for a beam of yellow laser light (580 nm) passing through a circular aperture of diameter 4 mm is calculated using the formula sinθ = 1.22(λ/d). The wavelength λ is converted to millimeters (0.00058 mm), and the diameter d is 4 mm. The correct calculation involves finding sinθ, taking the inverse sine to determine θ, and recognizing that the angular width is defined as the full angle from one minimum to the diametrically opposite minimum.

PREREQUISITES
  • Understanding of diffraction principles
  • Familiarity with the sine function and inverse sine calculations
  • Knowledge of laser light properties, specifically wavelength
  • Basic skills in unit conversion (e.g., nm to mm)
NEXT STEPS
  • Study the principles of diffraction and interference patterns
  • Learn about the Rayleigh criterion for resolution
  • Explore the effects of aperture size on diffraction patterns
  • Investigate the application of diffraction in optical instruments
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Physics students, optical engineers, and anyone interested in understanding diffraction phenomena and laser applications.

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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!
 

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