Calculating Minimum Width for 5 Interference Maxima

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SUMMARY

Ramon's problem involves calculating the minimum width of a screen to display five interference maxima using a double slit setup. The coherent light source has a wavelength of 554 nm, and the slit separation is 1.5 mm, with the screen positioned 90 cm away. The correct application of the formula λ/s = w/D reveals that the width between maxima should be calculated as 5w, leading to the conclusion that the initial misunderstanding stemmed from misinterpreting the number of maxima required. The correct interpretation results in using 4w for the total width calculation.

PREREQUISITES
  • Understanding of wave optics principles, specifically interference patterns.
  • Familiarity with the double slit experiment setup and calculations.
  • Knowledge of unit conversions, particularly between nanometers and millimeters.
  • Proficiency in algebraic manipulation of equations.
NEXT STEPS
  • Review the principles of wave interference in optics.
  • Study the double slit experiment and its mathematical formulations.
  • Learn about unit conversions in physics, focusing on wavelength measurements.
  • Practice solving problems involving interference patterns and maxima calculations.
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Students studying physics, particularly those focusing on optics, as well as educators seeking to clarify concepts related to interference patterns in wave mechanics.

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Homework Statement



Ramon has a coherent light source with wavelength 554 nm. He wishes to send light through a double slit with slit separation of 1.5 mm to a screen 90 cm away. What is the minimum width of the screen if Ramon wants to display five interference maxima?


Homework Equations



λ/s = w/D

λ= wavelength (554nm - converted to 5.54e-4 mm)
s= slit separation (1.5mm - provided by question)
w= width between maxima (use 5w do to question asking for 5 interference maxima)
D= distance to screen (90cm - converted to 900mm provided by question)

The Attempt at a Solution



Given that three of the four variables are known values, this should be simple as plug and solve. For some reason it is not liking the answer I am providing. The left side of the equation is simply 5.54e-4 / 1.5 which one would set equal to 5w / 900. Where am I going wrong here? Thanks in advance!
 
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Follow up: Figured it out. Initially thought of the question as asking about 5 maxima per side (thus 10 total). One maxima in the center, two per side, 5 total. w * 4 yields correct value.
 

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