Diffraction Grating Homework: Find the Distance of Bright Fringes

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SUMMARY

The discussion focuses on calculating the distance between the first-order bright fringes produced by red (λ = 650 nm) and green (λ = 532 nm) laser beams using a diffraction grating with 400 slits/mm. The initial calculation yielded a distance of 0.10856 m, which was identified as incorrect due to the assumption of a "small angle approximation." Participants emphasized the need to verify the angles of diffraction for both wavelengths to ensure accurate results.

PREREQUISITES
  • Understanding of diffraction grating principles
  • Familiarity with the wave nature of light
  • Knowledge of the small angle approximation in physics
  • Ability to perform calculations involving wavelengths and distances
NEXT STEPS
  • Review the derivation of the diffraction grating formula
  • Learn about the significance of the small angle approximation in optics
  • Explore the effects of varying slit density on diffraction patterns
  • Investigate the relationship between wavelength and fringe separation
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Barry Melby
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Homework Statement


You shine a red (λ = 650 nm) laser beam and a green (λ = 532 nm) laser beam at a diffraction grating that has 400 slits/mm to create an interference pattern on a wall 2.30 m from the grating. If the two lasers are directly on top of each other, how far apart are the two m = 1 bright fringes from each other?

Homework Equations

The Attempt at a Solution



(650*10^-9)(2.30) / (1/400)(.001) - (532*10^-9)(2.30) / (1/400)(.001) = 0.10856 m

This is incorrect, however. What did I miss?
 
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You calculation appears to assume a "small angle approximation". Check to see if the angles of diffraction for the two wavelengths are "small".
 

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