Fringe Radius Relation for Small Times t

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SUMMARY

The relationship between the fringe radius r and time t for small times t in the context of Newton's rings is defined by the equation r = (2TR)^(1/2). This equation holds true in general, not just for fringe patterns. The setup involves a spherical convex lens placed on a flat glass surface, which creates the necessary conditions for observing this relationship. A diagram illustrating the quantities r, t, and R is essential for a clearer understanding of the geometry involved.

PREREQUISITES
  • Understanding of Newton's rings and interference patterns
  • Familiarity with basic geometric optics
  • Knowledge of the relationship between radius, time, and curvature in optics
  • Ability to interpret and create diagrams related to optical setups
NEXT STEPS
  • Study the derivation of the fringe radius equation in Newton's rings
  • Explore geometric optics principles related to spherical lenses
  • Learn about interference patterns and their mathematical descriptions
  • Examine practical applications of Newton's rings in optical testing
USEFUL FOR

Students and professionals in physics, particularly those focusing on optics, as well as educators seeking to explain the principles of interference and fringe patterns.

Ciato
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1. Show that for t<<R, the radius r of a fringe is related to r= (2TR)^1/2

I'm not sure what the relevant equations are, that would be the problem. A gentle shove in the right direction would be appreciated, I've been looking for exactly how to prove it and I can't. ^_^ Thanks for any help!
 
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This relationship is true in general, not just for fringes. Examine the geometry of the Newton's rings set up: A spherical convex lens placed upon a flat piece of glass. Draw a diagram with the quantities r, t, and R indicated.
 

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