Minimum Mirror Height for Full Reflection
To determine the minimum height of a plane vertical mirror required for a person to see their full reflection, we use basic principles of light reflection.
Understanding the Reflection Principle
A person can see their complete image in a plane mirror if the mirror's height is at least half of the person's height. This is independent of the distance between the person and the mirror. The key is the geometry of light rays reflecting from the top of the head and the bottom of the feet to the observer's eyes.
Calculation
Given:
- Person's height ($H_{person}$) = 6 feet
The minimum required height of the mirror ($H_{mirror}$) is calculated as:
$ H_{mirror} = \frac{H_{person}}{2} $
Substituting the value:
$ H_{mirror} = \frac{6 \text{ feet}}{2} $
$ H_{mirror} = 3 \text{ feet} $
Conclusion
Therefore, the minimum height of the plane vertical mirror needed is 3 feet.
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