To determine the minimum length of a mirror required for a person to see their full image, we need to understand the physics principle involved. The principle is related to the reflection of light in plane mirrors.
When a person stands in front of a plane mirror, their full height can be seen if the mirror is positioned such that light rays from the top and bottom of the person can reflect into their eyes. The key point here is that you don't need the mirror to be as tall as the person to see the full image. Instead, the mirror needs to be positioned so that it covers the top half of the person’s view because of the geometry of light reflections.
Concept of Reflection: When light reflects off a plane mirror, the angle of incidence is equal to the angle of reflection. This geometric principle implies that only half of the mirror's length is needed to reflect light from the top and bottom of the person’s body to their eyes.
Geometric Explanation: When standing upright and looking straight into a mirror, the person’s eyes will see their feet in the lower half of the mirror and their head in the upper half. Therefore, a mirror with a height of half the person’s height is sufficient.
Calculation: Since the man is 6 feet tall, the minimum mirror length needed is half of 6 feet, which is:
3 \text{ feet}
Conclusion: Thus, the minimum length of the mirror required for a 6-foot-tall man to see his full image is 3 feet.
Therefore, the correct answer is 3 feet.
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