Curved glass and Newton's Rings

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SUMMARY

The discussion focuses on calculating the radius R of the outermost dark ring in a Newton's Rings pattern formed by a curved glass with a radius of r=10m, using light with a wavelength of 654 nm. The problem states that there are 100 dark fringes, excluding the central dark spot. The relevant hint indicates that for small angles, Tan(theta) can be approximated as theta in radians. The equation Sin(theta) = m * λ / W is referenced, although it is primarily used for single slit diffraction, indicating a need for a more suitable approach for this specific problem.

PREREQUISITES
  • Understanding of Newton's Rings and their formation
  • Familiarity with wave optics concepts, particularly interference patterns
  • Knowledge of small angle approximations in trigonometry
  • Ability to manipulate equations related to wave phenomena, such as Sin(theta) = m * λ / W
NEXT STEPS
  • Research the derivation of the formula for the radius of dark rings in Newton's Rings
  • Study the principles of interference and diffraction in wave optics
  • Explore the application of small angle approximations in optics
  • Investigate the relationship between wavelength and fringe spacing in interference patterns
USEFUL FOR

Students studying optics, physics educators, and anyone interested in wave interference phenomena, particularly in the context of Newton's Rings.

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Homework Statement


A piece of curved glass has a radius of r=10m and is used to form Newton's Rings. Not counting the dark spot in the center of the pattern, there are one hundred dark fringes the last one on the outer edge of the curved piece of glass. The light being used has a wavelength of 654 nm in a vacuum. What is radius R of the outermost dark ring in the pattern?

Hint:r >> R you may assume Tan(theta)= theta for small angles, where theta must be expressed in radians.
lamda = 654 E-9 m= 100

Homework Equations



the only equation that I can find that is even close is Sin(theta)= m* lamda/ W that is use for single slit diffraction. I really do not know how to set this up. The hint is no help to me at all.
 
Last edited:
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I believe the following page should aid you.

http://www.fas.harvard.edu/~scdiroff/lds/LightOptics/NewtonsRings/NewtonsRings.html
 

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