Does Focal Length Differ for Convex Lenses?

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Discussion Overview

The discussion revolves around the focal length of convex lenses and mirrors, exploring whether the same principles apply as with concave lenses and mirrors. Participants examine the relationships between radius and focal length, and the implications of sign conventions in optics.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant asserts that for concave lenses, the focal length is half the radius of the circle and questions if this applies to convex lenses as well.
  • Another participant challenges this assertion, stating that the rule for concave lenses does not apply to lenses in general.
  • A third participant introduces the lensmaker's equation, suggesting that it is the appropriate method to determine focal length for lenses.
  • A later post clarifies that the initial statement was meant to refer to concave mirrors instead of lenses.
  • One participant confirms that the focal length for convex mirrors is indeed half the radius but notes that the sign of the focal length is negative due to the nature of reflection.
  • Another participant elaborates on the sign convention, explaining that a convex mirror's focal length must be negative because the reflected beam diverges from a virtual source.

Areas of Agreement / Disagreement

Participants express disagreement regarding the application of focal length rules between concave and convex lenses and mirrors. There is no consensus on whether the same principles apply across these different optical elements.

Contextual Notes

There are unresolved assumptions regarding the definitions of focal length and radius in the context of different optical systems, as well as the implications of sign conventions in optics.

Who May Find This Useful

This discussion may be of interest to students and professionals in optics, physics, and engineering, particularly those exploring the properties of lenses and mirrors.

fromthepast
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I know that for concave lenses, the focal length is one half the length of the radius of the circle.

Is this also true for convex lenses?

Thanks
 
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fromthepast said:
I know that for concave lenses, the focal length is one half the length of the radius of the circle.
That's not true. Similar rule applies to mirrors, but not to lenses.
 
What I meant to say was:

"I know that for concave MIRRORS, the focal length is one half the length of the radius of the circle.

Is this also true for convex MIRRORS?"
 
Yes, it is.
Just draw yourself a picture how the light reflects from the spherical surface...
 
The number is the same for the same radius, but the sign flips - a convex mirror has a negative focal length, with the usual sign conventions. This makes sense if you think about it - a collimated object beam has the object at infinity, but the reflected beam diverges from a virtual source with a negative image distance. Therefore the focal length must be negative.
 

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