Mirror Height for Self-Reflection at Distance D for H

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SUMMARY

The minimum height of a mirror required for a person of height H standing at a distance D to see their full reflection can be calculated using geometric principles. The mirror height must be at least half of the person's height (H/2) to ensure that the angle of reflection allows for a complete view from head to toe. The distance D influences the angle of incidence and reflection, but does not change the required mirror height. Therefore, the formula for the minimum mirror height remains consistent regardless of the distance from the mirror.

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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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