His eyes are 1.83 m above the floor, and the top of his head is 0.15 m higher. Find the height above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet.

 y_lower = 0.915 m,   y_superior = 1,905 m

Explanation:

In this exercise we use the law of reflection for a flat mirror.

         θ’= θ

To see the feet of the person a ray of light that part of them must reach the bottom of the mirror and its reflection has to reach the eyes.

As the law of reflection the incident and reflected angles are equal, the distance from the floor to the point where the two rays (incident and reflected) touch the mirror must be symmetrical, oses from the floor

           y = 1.83 / 2

           y = 0.915 m

To see the head, a ray of light that comes from the tip of the head and is reflected in the mirror must reach the eyes. As the head is 0.15 m above the eyes and the incident and reflected rays have the same angle, the mirror must be at half the height, that is, the mirror is 0.075 m below the tip of the head.

In summary

* the bottom of the mirror is 0.915 m from the ground

* the top of the mirror is at 1.83 + 0.075

                 y_superior = 1,905 m

ground

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