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

[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?

 

[mjc123]

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

 

[Lnewqban]

 

[robphy]

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).

 

[DaveE]

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.

 

[robphy]

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”?