13.1.6 | revision #17985 | Savchenko Solutions

Statement

13.1.6. Height of a person $$h$$ . What is the minimum height that a mirror needs to
reach in order to see its full-length image?

Solution

For problem $13.1.6$ — For problem $$13.1.6$$

Lets say that the eyes are a distance

$b$

above the ground and that the forehead is

$a$

long. We know that the angle of incidence is equal to the angle of reflection, so the top of the forehead(the highest point of the body) is reflected at a height of

\frac{a}{2}

above the eyes before travelling into the eyes(Look at the figure above). The same argument can be given for the lower section of the body, so the mirror is

\frac{b}{2}

is below the eyes. the height of the mirror is

\frac{b}{2} + \frac{a}{2} = \frac{a+ b}{2}

and since

$a+b= h$

the height is:

\frac{h}{2}

To get the size of such a 2D object, its only important to look at the extreme points(top and bottom for instance).

Answer

[ $\frac{h}{2}$ ]