A plane mirror is placed along a positive x-axis facing along a positive y-axis. The equation of the linear object is \[x = y\]. What is the equation of its image?
A. \[x = y\]
B. \[x + y = 0\]
C. \[2x + y = 0\]
D. None of these

Hint: The image formed by the plane mirror is laterally inverted. Also, the distance of the image from the plane mirror is equal to the distance of the object.

Complete step by step answer:
To answer this question, you need to understand the image formed by the plane mirror. The image formed by the plane mirror is virtual, erect, laterally inverted and of the same size as the object.

Also, the distance between the object from the plane mirror is the same as the distance between image and the plane mirror.

Therefore, the x-coordinate of the equation of object does not change for the equation of image formed by the plane mirror.

The given equation of the linear object is \[x = y\]. That implies, the height of the image \[y\] is the same as the distance of the mirror on the x-axis.

As the mirror is facing the positive y-axis, its image is facing the negative y-axis. Therefore, the y-coordinate will become \[ - y\]-coordinate.

Since the image formed by the plane mirror is inverted and as of the same size as the object, the equation of the image formed by the plane mirror will be,
\[x = - y\]
\[ \Rightarrow x + y = 0\]

So, the correct answer is “Option B”.

Note:
The properties of plane mirror and spherical mirror are different.
Do not misunderstand between these two.
Note that the radius of curvature of the plane mirror is infinite.