Radius of Curvature: Definition & Meaning

  • Context: Undergrad 
  • Thread starter Thread starter mkbh_10
  • Start date Start date
  • Tags Tags
    Curvature Radius
Click For Summary
SUMMARY

The radius of curvature is defined as the radius of the arc of a spherical surface, specifically for mirrors and lenses. For a concave mirror, the radius of curvature is equal to 2f, where f is the focal length. However, for lenses, the radius of curvature can differ between the front and back surfaces and is not universally equal to 2f. Understanding the significance of the radius of curvature is crucial for optics, as it directly relates to the behavior of light through curved surfaces.

PREREQUISITES
  • Understanding of focal length in optics
  • Basic knowledge of spherical mirrors and lenses
  • Familiarity with geometric optics principles
  • Ability to interpret optical diagrams
NEXT STEPS
  • Research the relationship between focal length and radius of curvature in concave mirrors
  • Study the differences in radius of curvature for convex and concave lenses
  • Learn about the derivation of lens maker's formula
  • Explore practical applications of radius of curvature in optical design
USEFUL FOR

Students of physics, optical engineers, and anyone interested in the principles of lens and mirror design will benefit from this discussion.

mkbh_10
Messages
217
Reaction score
0
What is radius of curvature and why is it equal to 2f where f is the focal length of a lens or a mirror ?
 
Science news on Phys.org
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.
 

Attachments

  • mirror.JPG
    mirror.JPG
    4.1 KB · Views: 805
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.
 
Last edited:
  • Like
Likes   Reactions: gracy
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.
 

Similar threads

Undergrad Sine laws of spherical singlets
  • · Replies 72 ·
3
Replies
72
Views
6K
Undergrad Pentaprism with magnification, which surface is curved?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Spherical aberration in Biconvex lens
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Understanding magnification of concave mirrors for near-eye situation?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad About a concave mirror with a large focal length (1000mm)
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad Focusing UV light from a 275nm LED down to a small spot
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Virtual and real image with concave mirror at 45 degrees
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Position of the principal points of a telephoto lens system
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How to Calculate Radius of Curvature from Thin Film Interference?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Coinciding of 2F and C in ray diagram of lenses
  • · Replies 12 ·
Replies
12
Views
22K