Question

Figure 34-31 shows a coordinate system in front of a flat mirror, with the x-axis perpendicular to the mirror. Draw the image of the system in the mirror. (a) Which axis is reversed by the reflection? (b) If you face a mirror, is your image inverted (top for bottom)? (c) Is it reversed left and right (as commonly believed)? (d) What then is reversed?

Short answer

(a) The x-axis is reversed by the reflection.

(b) If you face the mirror, then the image is not inverted.

(c) No, the image is not reversed left or right.

(d) Only the perpendicular i.e. x-axis is reversed.

Step-by-step solution

The given data:

A coordinate system placed in front of a mirror is given.

Understanding the concept of properties of the flat mirror:

According to the laws of reflection, the angle of reflection is equal to the angle of incidence. The image is obtained behind the plane which is present in the mirror. This process of obtaining a mirror image that is virtual and upright is known as a plane mirror reflection.

If you stood in front of a mirror, you would see your image. When the light rays coming from you hit the smooth surface of the mirror, they are reflected back at the same angle. Your eyes will see these reflected light rays as a mirror image.

When an item is reflected in a plane mirror, an image is created that is virtual, upright, facing left to right, and the same size as the thing.

(a) Calculation of the axis reversed by the reflection:

In the flat mirror reflection, the axis perpendicular to the mirror only gets reversed.

In this case, the x-axis is perpendicular.

The initial coordinates system is $+x,+y,+z$.

As you know, the image formed by a flat mirror is equally placed on the opposite side of the mirror with coordinates signs changing as per the concept of a coordinate system.

Again, as per the given figure, the mirror is placed on the axis perpendicular to it while in a parallel form to the y-axis and the z-axis.

Thus, after the reflection, the new coordinate system is given as follows:

$-(+x),+y,+z=-x,+y,+z$

Hence, the image distance is only reversed by the x-axis after the reflection.

(b) Calculation of the behavior after you face your mirror:

If you stand in front of the mirror, then your image formed will be exactly at a parallel distance to me on the opposite side of the mirror. Thus, only your image distance is equally opposite from the origin to the oppositex-axis but still remains unchanged in the y-axis image coordinate as the reflection is only reversed by the x-axis as per discussions in part (a).

Hence, there will be no change.

(c) Calculation for knowing if the image is reversed or not:

As per the question, you need to check the left and right sides of your image with the flat mirror. These directions indicate the coordinates of thez-axis that remains unchanged as per the discussions based on part (a).

Hence, there is no change in the left and right directions of the image.

(d) Calculation of the object that is reversed:

As per the detailed discussion in part (a), you can see that the image is reversed in the direction which is perpendicular to the mirror axis placement. As here, the mirror is placed perpendicular to thex-axis, thus the image is only inverted or reversed in that direction only.

Hence, only the perpendicular axis to the mirror is reversed i.e., the x-axis from calculations of part (a).