Calculating Single Slit Diffraction Width with 630 nm Light

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SUMMARY

The discussion focuses on calculating the width of a single slit using 630 nm light and the resulting diffraction pattern. The linear distance between the first and second dark fringes is given as 12 cm, with the screen positioned 2.8 m away. The correct formula to determine the slit width (W) is W = λm / sin(θ), where λ is the wavelength and m is the order of the dark fringe. The final calculated width of the slit is 29.4 micrometers, although the initial attempt was incorrect due to a miscalculation involving the factor of 2.

PREREQUISITES
  • Understanding of single slit diffraction principles
  • Familiarity with trigonometric functions, specifically arctan
  • Knowledge of the wavelength of light and its application in diffraction calculations
  • Ability to manipulate and solve equations involving sine functions
NEXT STEPS
  • Review the derivation of the single slit diffraction formula
  • Practice calculating slit widths using different wavelengths and distances
  • Explore the impact of slit width on diffraction patterns
  • Learn about higher-order dark fringes and their calculations
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Students studying optics, physics educators, and anyone interested in understanding diffraction phenomena in wave mechanics.

muffintop
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Homework Statement


A single slit is illuminated with 630 nm light, and the resulting diffraction pattern is viewed on a screen 2.8 m away.
If the linear distance between the first and second dark fringes of the pattern is 12 cm, what is the width of the slit?

Homework Equations


y=Ltan\theta
W = \lambda m / sin \theta

The Attempt at a Solution


theta = arctan (.12/2.8) = 2.45
W = 630 x 10^-9 x 2 / sin 2.45
 
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Looks good.
 
I got 29.4 micrometers. It's wrong though.
 
muffintop said:
W = 630 x 10^-9 x 2 / sin 2.45
Oops... I missed that factor of 2 before. Why is it there?

Hint: Write expressions for the first dark fringe position and the second dark fringe position, then subtract.
 
I got it thank you so much!
I always get my "m" values wrong.
 

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