Interference pattern, wavelength

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SUMMARY

The discussion centers on calculating the wavelength of monochromatic light based on an interference pattern created by two slits separated by 127 µm and a screen distance of 1.14 m. The formula used is wavelength = (dsinθ) / m, where θ is derived from the tangent function. A participant incorrectly identified the variable m as the number of slits, while it actually represents the order of the fringes, starting from m=0 for the central bright fringe. The correct approach involves using m values such as 0, 1, or 2 to represent the first, second, and subsequent bright fringes.

PREREQUISITES
  • Understanding of wave interference principles
  • Familiarity with trigonometric functions, specifically tangent and sine
  • Knowledge of the double-slit experiment setup
  • Ability to manipulate equations involving wavelength and fringe order
NEXT STEPS
  • Study the double-slit experiment and its implications in wave optics
  • Learn how to derive and apply the interference pattern equations
  • Explore the significance of fringe order (m) in interference patterns
  • Investigate the effects of slit separation and distance on wavelength calculations
USEFUL FOR

Students studying physics, particularly those focusing on wave optics, as well as educators and anyone interested in understanding the principles of light interference and wavelength determination.

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Homework Statement


Suppose the interference pattern shown in the figure is produced by monochromatic light passing through two slits, with a separation of 127 µm, and onto a screen 1.14 m away. What is the wavelength?
28-34.gif



Homework Equations


wavelength = (dsin[tex]\theta[/tex]) / m
y=Ltan[tex]\theta[/tex]


The Attempt at a Solution


[tex]\theta[/tex]= arctan (y/L) = arctan (.023 / 1.4) = .941
then plugged it into get wavelenth. i used m = 2 for 2 slits
wavelenth = 127 x 10^-6m x sin .941 / 2

i think I have m wrong?
 
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i used m = 2 for 2 slits
m is not the number of slits. It is the order of the fringes starting from m=0 for the central bright fringe.
 

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