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Show that the minimum size of a plane mi...

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.

Text Solution

Verified by Experts

Let HF be the height of the man and E be the eye level. Draw the rays `HM_1` and `FM_2` incident at the edges of the mirror. Complete the ray diagram as shown in Fig. It is self-explanatory if you consider lengths x and y as shown in the figure.
Aliter:
`Delta EM_1M_2 and DeltaEH^(')F^(')` are similar
`:. (M_1M_2)/(H^(')F^('))=z/(2z)` or `M_1M_2=H^(')F^(')//2=HF//2`
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