Solved Problem on Flat Mirrors

An observer O is looking at a flat mirror E, as shown in the figure. Which of the objects listed from 1 to 5 can he see by reflection in the mirror?

Construction of the field of vision:

Points A and B are the ends of the mirror E, from the point where the observer is, we draw a straight line passing by point A (Figure 1).

Figure 1

We draw another line from O and passing through point B (Figure 2).

Figure 2

In the same direction of the mirror, we draw the straight segment \( \overline{AA'} \) (Figure 3).

Figure 3

From the O, perpendicular to the segment \( \overline{AA'} \), we draw a straight line and mark the point the O' behind the mirror and at the same distance of the point O (Figure 4).

Figure 4

From point O', we draw a straight line passing by point A (Figure 5).

Figure 5

Finally, we draw a straight line from the O' passing by point B. The field delimited by the lines from O' and the mirror, in gray in Figure 6, determines the field of vision. The observer can see by reflection the objects contained there.

Figura 6

Solution

Objects visible by the observer by reflection will be the numbers 1, 2 and 5.

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