https://file.aiquickdraw.com/mathbot/file/1726862717591hj27s99f.jpeg

The problem here involves Nancy trying to use a small plane mirror to see the full image of a man standing behind her. The given details are:

- The man is 1.8 meters tall.
- The man is 2.4 meters behind Nancy.
- The mirror is 10 cm (0.1 meters) long.
- Nancy’s eyes are 1.5 meters above the ground.

We need to calculate the maximum distance between Nancy and the mirror for her to see the full image of the man, who is 2.4 meters behind her.

### Key Principles:
- In a plane mirror, the height of the image appears to be the same as the height of the object.
- For Nancy to see the full image of the man, the mirror must allow light from both the top and bottom of the man’s reflection to reach Nancy’s eyes.
- The angle of incidence equals the angle of reflection, meaning that the distance and angles involved can be treated geometrically.

We need to find the correct geometric configuration to calculate the distance Nancy must stand from the mirror to capture the man's full reflection.

Let me now calculate the required distance using geometry.The maximum distance between Nancy and the mirror for her to see the entire image of the man is approximately **0.8 meters**. 

This distance ensures that the light reflecting from both the top and bottom of the man’s image can reach Nancy's eyes.

### Do you have any further questions or need details on any part of the solution?

Here are 5 related questions to consider:
1. How would the required distance change if the mirror were larger or smaller?
2. What would happen if the man were standing further behind Nancy?
3. How does the position of Nancy’s eyes affect the solution?
4. What would be the effect if the mirror were angled instead of held vertically?
5. How would the geometry change if the man were taller or shorter?

**Tip:** In mirror problems, remember that the apparent image distance behind a plane mirror is equal to the actual distance in front of it.

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 between Nancy and a mirror to see the full image of a person standing behind her. This problem explores key geometric and optical principles, including the law of reflection and properties of plane mirrors. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation