Question

Show that the minimum size of a plane mirror required to see the full image of an observer is half the size of that observer.

Answer 1

In the diagram, H'-head ,F'-Feet

$\Delta E{M}_1{M}_2$ and $\Delta E{H}^{\prime }{F}^{\prime }$ are similar.

$\frac{M_1{M}_2}{H^{\prime }{F}^{\prime }}=\frac{z}{2z}$

$M_1{M}_2=\frac{H^{\prime }{F}^{\prime }}{z}=\frac{HF}{z}$

Minimum size of the plane mirror is half size as that of observer.