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I'm getting confused with conventions. I was wondering if this logic is correct:

If an image appears on the same side of an object, then we use a negative focal length for determining information about the image's distance, the possible power, the object's distance, etc.

If an image appears on the opposite side of an object, the focal length is positive.

Under this logic, concave mirrors and diverging lens have negative focal lengths. Is this true?

Also, I think it would be appropriate to assume this is in the context of very rudimentary optics, so the thickness of the lens/mirrors is very small and minuscule in terms of qualitative analysis.

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    $\begingroup$ Almost. "image appears on the same side of an object" is not quite what a negative focal length is - more specifically, a diverging lens will have a negative focal length. In composite lens systems, there's no telling where the image ends up... Where did you learn about these things? What made you doubt your understanding? $\endgroup$
    – Floris
    Jan 23 '16 at 1:34
  • $\begingroup$ "If an image appears on the same side of an object, then we use a negative focal length for determining information about the image's distance," is correct for lens and incorrect for mirrors. The sign conventions of ray optics are detailed and have to be followed with care for everything to work out. $\endgroup$ Jan 23 '16 at 21:21
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The concave mirror will form a real image, so by convention it's focal length is positive. The diverging lens does not form a real image, but a virtual one, and thus is negative. Sometimes a negative lens is used for a beam expander for a laser and no focus is formed

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