A boy `1.5 m` tall with his eye level at `1.38 m` stands before a mirror fixed on a wall. Indicate by means of a ray diagram how the mirror should be positioned so that he can view himself fully. What should be the minimum length of the mirror ? Does the answer depend on the eye level ?

Explanation

In Fig., eye is at `1.38 m` from the foot `F`. Rays from foot can enter eye after reflection at `M_2`, whose height from ground is `(1.38)/(2) = 0.69 m`.
Again, eye is at `1.5 - 1.38 = 0.12 m` from head `H` . Rays from head can enter eye after reflection at `M_1`, whose height above the eye is `(0.12)/(2) = 0.06`
`:.` Minimum length of the mirror `= 0.69 + 0.06`
=`0.75 m`.
Minimum length of the mirror is thus always half of the length to be seen irrespective of eye level.
However, the position of the top and bottom edges of the mirror would depend on the eye level.
.