Final answer:
The minimum height of a plane mirror for a 1.70-m-tall person to view their entire image is half their height, which is 0.85 meters. This is based on the Law of Reflection in geometrical optics, allowing for the person's full height to be visible in the mirror.
Step-by-step explanation:
The minimum height of a plane mirror required for a 1.70-m-tall person to see their full image can be derived using the principles of geometrical optics, specifically the Law of Reflection.
According to this principle, a person can see their image in a plane mirror when the height of the mirror is at least one-half the height of the person. This means that for a person who is 1.70 meters tall, the height of the mirror should be at least 0.85 meters (which is half of 1.70 meters).
This is because the distance from a person's eyes to the top of their head (which can be more explicitly calculated as 1.65 m + 0.13 m for the eyes and head as given in the reference problems) is the same distance needed from the eyes to the top of the mirror.
Similarly, half the height of the person also relates to the distance needed from the eyes down to the bottom of the mirror. The combined distance from the top of the mirror to the person's eyes and from the bottom of the mirror to the person's eyes covers the full height of the person, thus allowing a full image to be seen.