Solve the Thin-Lens Equation: How & Why It Works

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SUMMARY

The thin-lens equation, expressed as 1/distance from lens to object + 1/distance from lens to image = 1/focal length, establishes a fundamental relationship in optics. This equation derives from the linear relationship between the distance a ray passes off-axis (r) and the angle it is kinked (\Delta\theta) as it passes through the lens, with the focal length (f) acting as the proportionality constant. By analyzing the angles for small deviations, the relationship between the object distance (o) and image distance (i) is clarified, leading to the derivation of the thin-lens formula.

PREREQUISITES
  • Understanding of basic optics principles
  • Familiarity with the concept of focal length
  • Knowledge of ray diagrams in lens systems
  • Basic trigonometry for small angle approximations
NEXT STEPS
  • Study the derivation of the thin-lens equation in detail
  • Explore applications of the thin-lens equation in optical systems
  • Learn about the impact of lens curvature on focal length
  • Investigate the differences between thin lenses and thick lenses
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Students of physics, optical engineers, and anyone interested in understanding the principles of lens optics and their applications in imaging systems.

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Hey. I understand the thin-lens equation and that it is 1/distance from lens to object + 1/distance from lens to image = 1/focal length. But, I was wondering how/why it works. If someone knows, I would appreciate the help. Thanks.
 
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The idea of a lens is to have a linear relationship between the distance a ray passes through off axis, and the amount the ray is kinked on passing through. Let us call the former quantity r and the latter \Delta\theta. The proportionality constant is f, the focal length. So we have
r=f\Delta\theta
If a ray comes from a point on axis a distance o upstream of the lens, and if \theta_o is the angle, then for small angles, \theta_o=r/o.
If this ray comes to a point on axis a distance i downstream of the lens, and if \theta_i is the angle, then for small angles, \theta_i=r/i.
Now, realize that
\Delta\theta=\theta_o+\theta_i
and you have your formula.
 
Thanks for the help.
 

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