Final answer:
A flat mirror produces a virtual image that is upright, same-sized, and located the same distance behind the mirror as the object is in front of it, due to the law of reflection rendering the magnification ratio as 1.
Step-by-step explanation:
To show that for a flat mirror hᵢ is equal to h₀, we need to consider the properties of the image formed by such a mirror. A flat mirror creates a virtual image that has the same characteristics as its corresponding object. This is due to the law of reflection, where the angle of incidence equals the angle of reflection. When light rays emanate from a point on an object and reflect off the mirror, they appear to originate from a point directly behind the mirror at the same distance.
Thus, using the concept of ray tracing illustrated in Figure 2.2, we can determine that the image formed is upright and located a distance (dᵢ) behind the mirror that is equal to the object distance (d₀) from the mirror. In this situation, the object and image heights are the same because the magnification of the image is directly proportional to the ratio of image distance to object distance, which is 1 in the case of a flat mirror.