Answer
See answers. The mirror equation and the lens equation are identical, but the sign conventions for the variables and the meaning of those signs have some differences.
Work Step by Step
The mirror equation and the lens equation are identical, but the sign conventions for the variables and the meaning of those signs have some differences.
The conventions are the same for focal length and for object distance. A positive focal length, $f\gt 0$, means that the lens or the mirror is converging. A negative focal length, $f\lt 0$, means that the lens or the mirror is diverging.
A positive object distance, $d_o \gt 0$, means that the object is real, and a negative object distance, $d_o \lt 0$, means that the object is virtual. For both mirrors and lenses, a real object is in front of the mirror or the lens (on the same side as the incoming light). A virtual object is on the other side.
A positive image distance, $d_i \gt 0$, means that the image is real, and a negative image distance, $d_i \lt 0$, means that the image is virtual. For a lens, a real image is behind the lens (on the opposite side of the lens from a real object, or, on the opposite side as the incoming light), and a virtual image is on the same side of the lens as a real object. For a mirror, a real image is in front of the mirror (on the same side as the incoming light), and a virtual image is behind the mirror (where there are no actual light rays).
