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There are three sorts of mirrors: plane mirror (Figure 1), converging mirror (Figure 2), and diverging mirror (Figure 3).
Figure 1. Plane mirror
Figure 2. Converging mirror
Figure 3. Diverging mirror
Properties of Image Produced by Mirrors
Properties of Image Produced by Mirrors
There are three properties of an image formed by a mirror: location, orientation, and size. If the image is located at the same side of the mirror as the object, it is real; otherwise, it is virtual. If the image is in the same direction that the object, it is upright; otherwise, it is inverted. If the image is smaller in size than the object, it is reduced; otherwise, it is magnified.
A plane mirror produces an upright, virtual image of the same size as the object. See an interesting discussion about the image formed in a plane mirror presented by the Physics Girl.
Ray Diagrams
Ray Diagrams
Any object is a source of light (either emitted or reflected) that can be modeled with numerous rays. These rays are represented by lines, which is why that branch of physics is called geometric optics.
In order to find an image created by a spherical mirror, just two characteristic rays are needed. The simulation below shows three:
The parallel ray (red) - the ray that originates in the very top of the object travels toward the mirror parallel to the axis of symmetry and is reflected back through the focal point (Figure 4)
The focus point ray (green) - the ray that originates in the very top of the object travels toward the mirror through the focal point and is reflected back parallel to the axis of symmetry (Figure 5)
The central ray (blue) - the ray that originates in the very top of the object travels toward the center of the mirror and is reflected back symmetrically (Figure 6)
Figure 4. Parallel ray
Figure 5. Focus point ray
Figure 6. Central ray
These rays intersect in one point and form the image. Notice the symmetry of the red and green ray; the parallel incidence ray is reflected back through the focal point, the one that passes through the focal point is reflected back parallel.
Concave Mirror Ray Diagram
Concave Mirror Ray Diagram
Only two rays are needed to create the image on a mirror. In the three diagrams below, the parallel and the central rays were used to find the image. Notice, that the three presented diagrams do not cover all possible cases of image formation.
Figure 7. Concave mirror, do > 2f
The object is placed beyond the center of curvature. The image produced by the concave mirror in this case is real, inverted, and reduced.
Figure 8. Concave mirror, f < do < 2f
The object is placed between the focal point and the center of curvature. The image produced by the concave mirror in this case is real, inverted, and magnified.
Figure 9. Concave mirror, do < f
The object is placed between the lens and the focal point. The image produced by the converging lens in this case is virtual, upright, and magnified.
Convex Mirror Ray Diagram
Convex Mirror Ray Diagram
The rules of finding the image produced by a diverging lens are the same. Notice that the image produced by the convex mirror is always virtual, upright, and reduced in size; the farther the object is from the mirror, the smaller image.
Figure 10. Convex mirror, do > 2f
Figure 11. Convex mirror, do < 2f
Mathematics of Spherical Mirrors
Mathematics of Spherical Mirrors
The math used to calculate distances from a mirror is quite simple. What may cause confusion, are the signs of the distance of the image and the focal length. By convention, the focal length of a concave mirror is positive and of a convex mirror is negative. All real distances are positive, while virtual ones are negative.
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