Radius of Curvature: Definition & Meaning

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Discussion Overview

The discussion revolves around the concept of radius of curvature, particularly its definition and its relationship to the focal length (f) of lenses and mirrors. Participants explore the implications of this relationship in both spherical mirrors and lenses, as well as the significance of radius of curvature in optics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the definition of radius of curvature and its equality to 2f for lenses and mirrors.
  • Another participant confirms that the radius of curvature for a spherical mirror is equal to 2f but expresses uncertainty regarding lenses.
  • Concerns are raised about the clarity of a diagram used in the discussion, specifically regarding the location of the center of the arc.
  • A participant emphasizes that for lenses, the radius of curvature may differ between the front and back surfaces and is generally not equal to 2f.
  • The significance of radius of curvature is questioned, with a participant suggesting it represents the radius of a circle or sphere that the surface is part of.
  • Clarification is provided that the formula and diagram discussed are applicable only to spherical concave mirrors.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the radius of curvature being equal to 2f for lenses, indicating a lack of consensus on this point. There is also uncertainty regarding the interpretation of diagrams related to the topic.

Contextual Notes

Some participants note that the definitions and relationships discussed may depend on specific contexts, such as whether the surface is part of a spherical mirror or a lens, and that the diagrams referenced may not clearly illustrate the concepts being debated.

mkbh_10
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What is radius of curvature and why is it equal to 2f where f is the focal length of a lens or a mirror ?
 
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You can check the definition in this : ttp://mathworld.wolfram.com/RadiusofCurvature.html

The radius of a spherical mirror is equal to 2f : that's right. But the lense : I am not sure.
You can see in the attached picture: AOF is an isosceles triangle.
 

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but looking at th diagram I don't see where the centre of that arc is.
 
mkbh_10 said:
What is radius of curvature and why is it equal to 2f where f is the focal length of a lens or a mirror ?

For a concave mirror see

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/mireq.html#c1

For a lens, the radius of curvature (it can be different for the front and back surfaces of a lens) is generally not equal to 2f. For the focal length of a lens see

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/foclen.html#c2

and

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lenmak.html#c1
 
What is the significance of radius of curvature ?
 
Imagine that the surface is part of a circle or sphere. The radius of curvature is the radius of that circle/sphere.
 
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whydoesitwork said:
but looking at th diagram I don't see where the centre of that arc is.

In my picture, the arc center is O because it is a part of a cicle. Remember that diagram and thurs formula only fits for a spherical concave mirror.

PS. Sorry I can not login my nick pixel01 because I forgot the pw and unfortunately the email address has been expired.
 

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