Find Distance for 1.2cm Circular Diffraction Pattern

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SUMMARY

The discussion centers on calculating the distance from a pinhole to a viewing screen for a circular diffraction pattern with a central maximum diameter of 1.2 cm, using a helium-neon laser with a wavelength of 633 nm and a pinhole diameter of 0.13 mm. The initial calculation yielded an incorrect distance of 1.23 m due to the inappropriate application of the formula Y = λx/b, which is not valid for circular apertures. The correct approach requires using the appropriate diffraction equations specific to circular apertures.

PREREQUISITES
  • Understanding of diffraction patterns and their formation.
  • Familiarity with the principles of wave optics.
  • Knowledge of the relationship between wavelength, aperture size, and distance in diffraction.
  • Ability to apply mathematical equations related to optical phenomena.
NEXT STEPS
  • Study the diffraction pattern equations specific to circular apertures.
  • Learn about the Rayleigh criterion for resolution in optics.
  • Explore the use of simulation tools for visualizing diffraction patterns.
  • Investigate experimental setups for measuring diffraction patterns in a lab environment.
USEFUL FOR

Students in physics, optical engineers, and anyone involved in experimental optics or wave phenomena who seeks to understand the principles of diffraction and its applications.

Plasmosis1
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Homework Statement



You want to photograph a circular diffraction pattern whose central maximum has a diameter of 1.2cm . You have a helium-neon laser (λ=633nm) and a 0.13-mm-diameter pinhole. How far behind the pinhole should you place the viewing screen?

Homework Equations



Y = λx/b
Y=radius of central maximum
b= slit diameter
x=distance from screen

The Attempt at a Solution



.012/2=633e-9*x/0.00013
x=1.23m <--- This answer is wrong. I don't know why.
 
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Plasmosis1 said:

Homework Statement



You want to photograph a circular diffraction pattern whose central maximum has a diameter of 1.2cm . You have a helium-neon laser (λ=633nm) and a 0.13-mm-diameter pinhole. How far behind the pinhole should you place the viewing screen?

Homework Equations



Y = λx/b
Y=radius of central maximum
b= slit diameter
x=distance from screen

The Attempt at a Solution



.012/2=633e-9*x/0.00013
x=1.23m <--- This answer is wrong. I don't know why.


The equation does not hold for a circular aperture. See http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/cirapp2.html#c2 or check your lecture notes.

Y =1.22 λx/b

ehild
 

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