Mirror Height for Self-Reflection at Distance D for H

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To determine the minimum height of a mirror for a person of height H standing at a distance D, the mirror must be at least half the height of the person. The line of sight from the eyes to the mirror and back creates angles that depend on the distance to the mirror. As the distance D increases, the angle of reflection changes, which can affect visibility. Therefore, the mirror's height should be calculated considering these angles to ensure the entire body is reflected. Proper calculations will ensure that the person can see themselves from head to toe.
Edgar White
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Hello,

I was wondering how to find the minimum height of a mirror so somebody of height H that is at a distance D of the mirror sees himself from head to toes.

Anybody can help me out ? Thanks !
 
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Consider that the angle of line of sight from the eye to the mirror and back to the person would be divided between the distance to the mirror and the distance back to the reflected image.

Also note that the angle of reflection changes as the distance changes.
 
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