Правка разделов «Statement», «Solution», «Answer»
en/13.1.6.md
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| ### Statement | |||
| − | $13.1.6.$ | ||
| + | $13.1.6.$ 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 | |||
|  | |||
| + | 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 | |||
| − | [Insert a concise answer or boxed result] | ||
| + | [$\frac{h}{2}$] | ||
| @@ -1,13 +1,14 @@ | |||
| ### Statement | ### Statement | ||
| $13.1.6.$ |
$13.1.6.$ 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 | ### Solution | ||
|  |  | ||
| 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 | #### Answer | ||
| [Insert a concise answer or boxed result] | [$\frac{h}{2}$] | ||