Question

The image formed by a plane mirror is always:
A. Real and erect
B. Virtual and erect
C. Real and inverted
D. Virtual and inverted

Answer 1

Hint: Making a diagram of the process, of how an image is formed by a plane mirror will help in understanding the problem. With the help of laws of reflection, we can make the ray diagram of how the rays emerge from the object and get reflected by the reflecting surface of the mirror and then reach the observer. By elongating the reflected rays that reach the observer, we find them to converge behind the mirror, forming the image. Analyzing the way the image is formed, will give us the solution.

Step by step solution:
Let’s first understand how the process of image formation on a plane mirror happens using a detailed diagram.

In this process we consider the rays to be emerging from only two points of the object, P and ${P}'$. So, let’s first consider the two rays that emerge from the point P at the base of the object. These two rays strike the mirror, and get reflected to the observer. Now, if those reflected rays were to be extended backward behind the mirror as made in the diagram, then it would seem that as though these sets of rays seem to originate from point Q. Hence, this is where the image of point P is located.
Similarly, upon repeating this process for point ${P}'$, we find its image to be formed at the point ${Q}'$. By considering the plane mirror to be exactly upright and perpendicular to the ground and parallel to the object $P{P}'$, using basic geometry, we can state that the image height $Q{Q}'$ is the same as the object height $P{P}'$. Hence, using the same process as above, making images of all points of the object, we will obtain an upright image of the object behind the mirror, having the same height as that of the object.
We also notice that the reflected rays appear to be coming directly from the image behind the mirror, to the observer. However, in reality, these rays are just reflections coming from the points from where they are reflected. Hence, the image formed behind the mirror is called a virtual image, because this image cannot be projected onto a screen. It means that these rays only appear to originate from a common point behind the mirror. However, if we walk behind the mirror, we won't find an image in reality behind the mirror.
Hence, a plane mirror will always generate a virtual and erect image, which is given by the Option B.

Note: It is important to remember, that during this whole process, the laws of reflection were used to make the ray diagrams. The rays emerging from the object and the way they are getting reflected from the reflecting surface of the plane mirror. Hence, the triangles formed such as PAB and QAB are similar triangles. Hence, the object and the image distances are equal: \[{{d}_{0}}={{d}_{i}}\]. Hence, the focal length of a plane mirror is always infinity, using the mirror formula: $\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}\Rightarrow \dfrac{1}{{{d}_{i}}}-\dfrac{1}{{{d}_{0}}}=\dfrac{1}{f}\Rightarrow 0=\dfrac{1}{f}\Rightarrow f=\infty $.