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The problem describes Nancy using a small plane mirror to see a man standing 2.4 m behind her. Nancy's eyes are 1.5 m above the ground, and the man is 1.8 m tall. The mirror Nancy holds is 10 cm (0.10 m) long.

To solve this, we can apply the principles of reflection from plane mirrors. For Nancy to see the full image of the man in the mirror, the mirror must cover the vertical extent from the top of his head (1.8 m above the ground) to his feet (0 m).

1. **Step 1: Half-size mirror rule**  
The key point here is that, for a plane mirror, the minimum size needed to see a full reflection of an object is half the height of the object being viewed. This is because the distance from the person’s eyes to the top and bottom of the object is reflected at an angle in the mirror.

2. **Step 2: Mirror positioning**  
- Nancy holds the mirror 1.5 m above the ground, meaning it reflects objects below her eye level.  
- The man is 1.8 m tall and stands 2.4 m behind Nancy.

3. **Step 3: Calculation of maximum distance for visibility**  
We need to calculate the maximum distance between Nancy and the mirror that will still allow her to see the full image of the man, considering the mirror is 0.10 m long.

Let me calculate that.The required mirror length to fully see the man should be **0.9 meters** based on the half-size mirror rule. However, the actual mirror is only 0.10 meters in length, which means it is far too small to reflect the entire image of the man.

Since the mirror's length is much shorter than required, Nancy will not be able to see the full height of the man in the mirror at any distance. Therefore, none of the distances between her and the mirror given in the problem choices would work for seeing the whole image.

Let me know if you'd like a more detailed breakdown or further clarification on any part of this solution!

Here are 5 related questions to think about:
1. How does the half-size mirror rule work in more detail for different object heights?
2. What happens if the mirror is not held vertically but at an angle?
3. How does the distance between the observer and the mirror affect the image size?
4. How does a concave or convex mirror change the reflection compared to a plane mirror?
5. Why can't Nancy see the full man if the mirror is smaller than required?

**Tip**: To see the full reflection of an object in a plane mirror, remember the mirror needs to be half the height of the object.

Nancy tries to use a small plane mirror to observe a man 2.4 m behind her. The man is 1.8 m tall. The mirror is 10 cm long. Nancy's eyes are 1.5 m above the ground. Assume Nancy holds the mirror vertically. What is the maximum distance between Nancy and the mirror for her to see the whole image of the man?

Learn how to calculate the maximum distance for observing a full image in a plane mirror. In this problem, a 1.8m tall man stands 2.4m behind Nancy, and she uses a 10 cm mirror. Understand the half-size mirror rule and reflection theorem to solve this high school-level geometry problem.

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