A flat mirror is one in which the reflection surface is completely flat.
Flat mirrors have a wide range of uses, from home to mirror as components of sophisticated optical instruments.
A flat mirror is represented by:
The main properties of a flat mirror are the symmetry between the object and image points and that most of the reflection that happens is regular.
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Mirrors are usually made of a well-polished metal surface. It is common to use a glass plate, where a thin layer of silver or aluminum is deposited on one side, making the other a mirror.
Construction of images in a flat mirror
To determine the image in a flat mirror, just imagine that the observer sees an object that appears to be behind the mirror. This is because the extension of the reflected ray passes through a virtual image point (PIV) "behind" the mirror.
In flat mirrors, the object and its image always have opposite natures, that is, when one is real the other must be virtual. Therefore, to obtain the image of a point object geometrically, it is enough to draw a straight line through it and symmetrically mark the image point.
Translation of a flat mirror
Considering the figure:
The top of the drawing shows a person at a distance from the mirror, then the image appears at a distance in relation to the mirror.
At the bottom of the picture, the mirror is moved to the right, causing the viewer to be at a distance mirror, causing the image to shift x to the right.
From the drawing we can see that:
That can be rewritten as:
But by the figure, we can see that:
Thus it can be concluded that whenever a mirror is translated parallel to itself, the image of a fixed object translates in the same direction as the mirror, but with a length equivalent to twice the length of the mirror translation.
If we use this equation, and measure its rate of change over a period of time, we can write the translation speed of the mirror and the image as follows:
That is, the image travel speed is twice the mirror travel speed.
When the observer also moves, the velocity when considered is the relative velocity between the observer and the mirror, rather than the translational speed of the mirror, ie: