How do you know if the focal length is positive or negative?

Click For Summary
SUMMARY

The discussion centers on determining the sign of the focal length in optics, specifically regarding spherical mirrors. It emphasizes that the designation of focal length as "positive" or "negative" is contingent upon established sign conventions for mirrors and lenses. The conversation highlights the importance of ray diagrams in identifying focal points, which are dictated by physics and geometry rather than conventions. Additionally, it notes that a concave mirror inherently indicates a positive focal length, while a convex mirror would suggest a negative focal length.

PREREQUISITES
  • Understanding of spherical mirrors and their properties
  • Familiarity with ray diagrams in optics
  • Knowledge of sign conventions in optics
  • Basic principles of light behavior when interacting with mirrors
NEXT STEPS
  • Research the sign conventions for focal lengths in optics
  • Study ray diagrams for concave and convex mirrors
  • Explore the physical meaning of focal points in optical systems
  • Learn about the differences between concave and convex mirrors
USEFUL FOR

Students of optics, physics educators, and anyone interested in understanding the behavior of light with mirrors and the implications of focal lengths in optical systems.

bluesteels
Messages
28
Reaction score
1
Homework Statement
An object 0.600 cm tall is placed 16.5 cm to the left of the vertex
of a concave spherical mirror having a radius of curvature of 22.0 cm.
(a) Draw a principal-ray diagram showing the formation of the image.
(b) Determine the nature (real or virtual)
of the image
Relevant Equations
none
In this problem, it doesn't tell you where is the focal length.

So how do you know if it is in front or behind the object?
 
Physics news on Phys.org
What do you know about the focal length of a spherical mirror?
 
2428px-Concave_mirror.svg.png
 
  • Like
Likes   Reactions: bluesteels
To answer the question in the title...
In optics, there are numerous sign conventions and definitions.
So, "positive" or "negative" depends on conventions (for mirrors and for lenses).

However, with ray diagrams,
the focal points are determined by the physics and the geometry (independent of the conventions).
 
Yes, I'm stumped too. "to the left of" isn't that helpful if there's no other left-right reference. Did you post the entire problem? Is there a drawing with left-right information? Like which way the mirror is oriented. I guess, worst case, you could solve it both ways.

I guess there is a weak convention in optics that rays start in the z-axis direction which is drawn from left to right (usually). Like @Lnewqban's drawing. So that would be my guess.

PS: Maybe I misunderstood. There is clear information about the focal length when they say the mirror is concave. Look that up. If the rays hit the other side of the sphere, they would have said convex.
 
It might help to ask yourself:

What happens to a light ray when it meets the mirror?

What is the physical meaning of the “focal point”?
 

Similar threads

Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 12 ·
Replies
12
Views
4K
Replies
5
Views
2K
Replies
4
Views
1K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 5 ·
Replies
5
Views
3K