Focal length equation from Radii of Curvature and refractive index of lens

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SUMMARY

The discussion centers on deriving the focal length equation for a biconvex lens based on its radii of curvature, thickness, and refractive indices. The user sought a reliable reference for this equation, which is typically found in optics textbooks like "Optics" by Eugene Hecht. The user also highlighted the need for a general version of the equation that incorporates the refractive index of the surrounding medium. Ultimately, they discovered a suitable source for their query through further research.

PREREQUISITES
  • Understanding of biconvex lens geometry
  • Familiarity with the lens maker's equation
  • Knowledge of refractive indices
  • Basic principles of optics
NEXT STEPS
  • Study the lens maker's equation for biconvex lenses
  • Research the concept of back focal distance in optics
  • Explore the derivation of the focal length equation in thick lenses
  • Read "Optics" by Eugene Hecht for comprehensive understanding
USEFUL FOR

Students of optics, optical engineers, and anyone involved in lens design and analysis will benefit from this discussion.

Snoopey
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Hi all,

I'm looking for an equation which will give me the focal length of a biconvex lens given that we know both Radii of curvature, the thickness of the lens and the refractive index inside and outside.

An equation is given on wikipedia here http://en.wikipedia.org/wiki/Focal_length as

d5d9b5b95cf3fd9ea7f2549ae4ee8fa6.png


I need something I can reference though and I can't see this equation anywhere else I look. Also I need a more general version of the equation which involves the refractive index of the substance surrounding the lens.
Could anyone point me to a derivation of this formula or lead me in the right direction?

I also need to find a legitimate source for the back focal distance shown on the same page of wikipedia:

30eebfeda11493b69809a64439377125.png


Thanks all!

EDIT: Found what I was looking for, just needed a bit more snooping!
http://physics.tamuk.edu/~suson/html/4323/thick.html
 
Last edited:
Science news on Phys.org
Any decent optics textbook (e.g. Hecht) should have that equation, in a chapter on thick lenses.
 

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