To determine the maximum and minimum heights at which a person can see the image of the top of the pole in the mirror, we need to visualize the scenario and apply some geometric reasoning. Let's break it down step by step.
Understanding the Setup
We have a pole that is 4 meters tall, and it is positioned 2 meters away from a vertical plane mirror. The mirror itself is 2 meters long, with its lower edge positioned 6 meters above the ground. The person is standing 4 meters away from the mirror, on the same horizontal line as the pole.
Visualizing the Image
When light reflects off the mirror, the image of the pole will appear to be at the same height as the actual pole, but behind the mirror. The height of the image can be calculated based on the height of the pole and the position of the mirror.
Calculating the Image Height
The top of the pole is at a height of 4 meters. The image of the top of the pole will appear at the same height of 4 meters behind the mirror. Since the lower edge of the mirror is at 6 meters, the image of the top of the pole will be visible in the mirror.
Determining Viewing Angles
To find the maximum and minimum heights from which a person can see the image, we need to consider the angles formed by the line of sight from the person's eyes to the image in the mirror.
- Maximum Height: The person can see the image of the top of the pole if they are looking from a height that allows them to see the top of the mirror. Since the mirror is 2 meters long and starts at 6 meters, the top of the mirror is at 8 meters. Therefore, the maximum height from which the person can see the image is 8 meters.
- Minimum Height: The minimum height is determined by the lowest point of the mirror. The lower edge of the mirror is at 6 meters. Therefore, the minimum height from which the person can see the image is 6 meters.
Final Heights for Viewing
In summary, the maximum height from which a person can see the image of the top of the pole is 8 meters, while the minimum height is 6 meters. This means that anyone standing between these two heights, looking towards the mirror, will be able to see the image of the top of the pole reflected in the mirror.
This scenario illustrates the principles of reflection and the importance of angles in determining visibility. By understanding how light behaves when it hits a reflective surface, we can solve various problems related to optics and geometry.
