# Minimum distance from the mirror should the boy be to see his full image

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A plane mirror with its bottom edge on the floor is tilted at an angle $\theta$
to the vertical (see figure). A boy whose eyes are at a height h above the
floor is standing in front of the mirror. At what minimum distance from
the mirror should the boy be to see his full image in the mirror?

To get the minimum d the rays should go parallel to floor and then get reflected to the boy eyes
Answer given = $(h\sec\theta)/2$

1 vote

The obvious trial value here is $\theta=0$. Then you can always see your feet, at any distance from the mirror. Your answer predicts $d=\infty$, which is what you expect. The official formula predicts $d=\frac12 h$, which is not what you expect. A sketch shows that you can still see your feet closer or further than $d=\frac12 h$.