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

• bluesteels
In summary, the conversation discusses the concept of focal length in optics and how it can be determined by both conventions and ray diagrams. There is a weak convention that rays start in the z-axis direction, and the fact that the mirror is concave also provides information about the focal length. The focal point is the point where a light ray meets the mirror and has a physical meaning in determining the behavior of light when it meets the mirror.
bluesteels
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?

What do you know about the focal length of a spherical mirror?

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”?

## 1. How do you determine the sign of the focal length?

The sign of the focal length can be determined by the direction in which the light rays converge or diverge. If the light rays converge, the focal length is positive, and if they diverge, the focal length is negative.

## 2. Can the sign of the focal length change?

Yes, the sign of the focal length can change depending on the type of lens or mirror being used. For example, a convex lens will have a positive focal length, while a concave lens will have a negative focal length.

## 3. How does the sign of the focal length affect the image formed?

The sign of the focal length determines whether the image formed is real or virtual. A positive focal length will produce a real image, while a negative focal length will produce a virtual image.

## 4. Are there any exceptions to the rule of determining the sign of the focal length?

Yes, there are a few exceptions. For example, in a concave mirror, the focal length is always negative, regardless of the direction of the light rays. Additionally, in some cases, the focal length may be considered positive or negative based on convention or the specific setup of the optical system.

## 5. How do you measure the focal length to determine its sign?

The focal length can be measured using various methods, such as the thin lens equation or by measuring the distance between the lens or mirror and the image formed. Once the focal length is determined, its sign can be determined using the rules mentioned in the first question.

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