Question

The magnification produced by a plane mirror is $+1$. What does this mean?

Answer 1

Recall that magnification is a quantity that relates the size of the image to the size of its object. Therefore, the number would denote the extent or magnitude of magnification, whereas the sign would indicate the orientation of the image with respect to the object. Remember that plane mirrors always form virtual images.

Formula used:
Magnification $M = \dfrac{image\;height}{object\;height}$

Complete answer:
Let us begin by understanding what magnification means in the context of a plane mirror.
In general, magnification suggests the increase or decrease in the size of an image produced by an optical system compared to its true size. It can also be expressed in terms how farther or nearer the image is to the optical system than the object distance. To this end, magnification for a plane mirror can be quantified as follows:

Magnification $M = \dfrac{image\;height}{object\;height}$
Now, we are given that the magnification produced by a plane mirror is $+1$
$\Rightarrow M = \dfrac{image\;height}{object\;height} = +1 \Rightarrow image\;height = object\;height$

Also, the “+” sign indicates that the image formed by the plane mirror is erect. A plane mirror forms erect images only when the image formed is virtual. Therefore, the image formed by the plane mirror is virtual, upright, same size as the object, and at the same distance from the mirror as the object.

Note:
It is often the case where the term inversion may be wrongly used instead of left-right reversal, in the context of images produced by a plane mirror. An image appears to be inverted when it seems to flip in the vertical direction when compared to the object. However, images formed by plane mirrors are not inverted. If you were to stand in front of the mirror, the image of your head and feet would be in the same orientation as yours, so would the ceiling and the floor. However, if you were to raise your right-hand, it would look like you were raising your left hand from the image’s point of view. This is called a left-right reversal. Therefore, do not get this confused with inversion.