Optics Equation: What Assumptions Lead to n1f1=-n2f2?

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SUMMARY

The equation n1f1 = -n2f2 is derived from Snell's Law under specific assumptions regarding optical systems. This relationship is particularly relevant in the context of field curvature, an optical aberration that affects image quality. Understanding this equation requires knowledge of the refractive indices (n1 and n2) and the focal lengths (f1 and f2) of the optical components involved. The discussion emphasizes the importance of these parameters in deriving the equation and its implications for optical design.

PREREQUISITES
  • Understanding of Snell's Law in optics
  • Knowledge of refractive indices in optical materials
  • Familiarity with focal lengths in lens systems
  • Concept of optical aberrations, specifically field curvature
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  • Research the derivation of Snell's Law and its applications in optics
  • Study the principles of optical aberrations and their effects on image quality
  • Explore the relationship between refractive indices and focal lengths in lens design
  • Investigate methods to correct field curvature in optical systems
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Optical engineers, physicists, and students studying optics who seek to deepen their understanding of lens behavior and optical aberrations.

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I keep seeing this equation pop up and I have no idea what it is or where it comes from.

n_{1}f_{1}= -n_{2}f_{2}

It looks like a take on snell's law, but what assumptions have to be made to get to this equation from snell's?
 
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The formula is related to an optical aberration called field curvature. See attachment.
 

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  • Curvature aberration.jpg
    Curvature aberration.jpg
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Thank you.
 

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