Deriving back focal length using Fermat's principle

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SUMMARY

The discussion focuses on deriving the back focal length of a plano-convex lens with a diameter of 200 mm, a central thickness of 20 mm, and a refractive index of 1.5. The user applies Fermat's principle, assuming equal travel time for light from the lens tip and center to the focal point. This approach is confirmed as valid for calculating the back focal length, which is a critical parameter in optical design.

PREREQUISITES
  • Understanding of plano-convex lens geometry
  • Familiarity with Fermat's principle of least time
  • Knowledge of optical refractive indices
  • Basic principles of lens focal length calculations
NEXT STEPS
  • Study the derivation of focal lengths for different lens shapes
  • Learn about the application of Fermat's principle in optics
  • Explore the impact of refractive index on lens performance
  • Investigate advanced lens design techniques using ray tracing software
USEFUL FOR

Optical engineers, physics students, and anyone involved in lens design and analysis will benefit from this discussion.

Woolyabyss
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Homework Statement


The plano-convex lens has a diameter of 200 mm and the central thickness of 20 mm. The edge thickness is zero and the refractive index of glass is 1.5. Find the following parameters of the lens: (i) the back focal length

Homework Equations


N/A

The Attempt at a Solution


I've attached my attempt below. I'm assuming the time taken for light to travel from the tip to the focal length is equal to the time taken to travel to the center to the focal length.
 

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