Two slit interference question dont know how to begin

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SUMMARY

The discussion centers on solving a two-slit interference problem involving a screen positioned 2.2 meters from two slits, with a distance of 1.6 mm from the central maximum to the second dark band. The key equations involve the relationship between path length difference and wavelength (λ), where destructive interference occurs at half the wavelength and constructive interference at whole number multiples of the wavelength. The phase difference is calculated as the path length difference divided by the wavelength, multiplied by 360 degrees. Participants emphasize the importance of understanding wave interference principles to derive the slit distance in terms of wavelength.

PREREQUISITES
  • Understanding of wave interference principles
  • Familiarity with the concept of wavelength (λ)
  • Knowledge of phase difference calculations
  • Basic grasp of trigonometry related to wave patterns
NEXT STEPS
  • Study the derivation of the two-slit interference formula
  • Learn about the relationship between slit separation and wavelength in interference patterns
  • Explore the concept of path length difference in wave mechanics
  • Investigate practical applications of interference patterns in optics
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Students studying physics, particularly those focusing on wave optics, as well as educators and anyone seeking to understand the principles of interference in light waves.

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Homework Statement


Two slit interference question: A screen is 2.2m from two slits. The distance from point P to point R (the central maximum to the 2nd dark band) is 1.6mm.
This is what the pattern looks like (l) means light band... (d) means dark band


......P...R
(d) (l) (d) (l) (d) (l) (d) (l) (d) (l) (d)



Homework Equations


Determine the distance between the slits in terms of wavelength (lamda)


The Attempt at a Solution



I don't know how to begin, so I will say what I know... The bands are produced because the light waves interfere either constructively or destructively, depending on path length difference (difference in distance from slit to screen for any two waves) , which effects the phase difference between each waveform. If path length difference is half the wavelength this will produce destructive inteference, because the amplitudes sum and will therefore cancel, producing dark band. If path length is whole number multiple of wavelength, it will produce light band -max intensity, because the amplitudes sum and intensity is proportional to amplitude.

I also know that phase difference is path length difference divided by wavelength times 360deg.

Homework Statement





Homework Equations


please help me to begin??


The Attempt at a Solution

 
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