Final answer:
The sign conventions for focal length in mirrors are that it is positive for concave (converging) mirrors and negative for convex (diverging) mirrors. Image distance is positive for real images and negative for virtual images.
Step-by-step explanation:
The sign conventions for the focal point in mirrors are essential in geometric optics to provide positive or negative values to quantify an optical system. In the context of mirrors, specifically spherical mirrors, different signs are assigned to the focal length (f) based on whether the mirror is concave or convex. Ray diagrams illustrate how parallel rays reflect off mirrors and either converge or appear to diverge at the focal point (F).
Concave Mirrors
For a concave mirror, which is a converging mirror, parallel rays that are incident upon the mirror surface are reflected through the actual focal point on the same side of the mirror. The focal length (f) for concave mirrors is considered positive.
Convex Mirrors
In contrast, a convex mirror, known as a diverging mirror, reflects parallel rays such that they seem to originate from a virtual focal point behind the mirror. Thus, the focal length (f) for convex mirrors is negative
Also, the image distance (di) is positive when the image is real and on the same side of the mirror as the object, but negative when the image is virtual and appears on the opposite side of the mirror.