Image Formation for Concave Mirrors

To view an object in any type of mirror, a person must sight along a line at the image of the object. All persons capable of seeing the image must sight along a line of sight directed towards the precise image location. As a person sights in a mirror at the image of an object, there will be a reflected ray of light coming from the mirror to that person's eye. The origin of this light ray is the object. A multitude of light rays from the object are incident on the mirror in a variety of directions; yet as you sight at the image, only a small portion of the many rays will reflect off the mirror and travel to your eye. To see an object in a mirror, you must sight at the image; and when you do reflected rays of light will travel from the mirror to your eye along your line of sight.
Not all people who are viewing the object in the mirror will sight along the same geometrical line of sight. The precise direction of the sight line depends on the location of the object, the location of the person, and the type of mirror. Yet all of the lines of sight, regardless of their direction, will pass through the image location. In fact, the image location is defined as the location where reflected rays intersect. Since all people see a reflected ray of light as they sight at an image in the mirror, then the image location must be the intersection point of these reflected rays.

In the animation above, an object is positioned above the principal axis of a concave mirror and somewhere beyond the center of curvature (C). The concave mirror will produce an image of the object which is inverted (positioned below the principal axis) and located between the center of curvature (C) and the focal point (F) of the mirror. Any person viewing this image must sight at this image position. The animation depicts the path of light to each person's eye. Different people are sighting in different directions; yet each person is sighting at the same image location. As seen in the animation, the image location is the intersection point of all the reflected rays.

Object Located Beyond the Center of Curvature

Ray diagrams are useful tools for determining the location of an image as produced by a concave mirror. To determine the location of an image using a ray diagram, at least two sets of incident and reflected rays must be constructed for strategic positions on the object. The image of an object is the location where light rays from that object intersect upon reflecting from a mirror. By constructing at least two sets of incident and reflected rays, this image location can easily be found.

If the object is represented by an arrow, then it is common practice to pick the two extreme positions (the top and the bottom of the arrow) as starting points for the incident and reflected rays. Ray construction will result in the determination of the image locations for these two extreme positions on the object. The complete image is merely an arrow connecting these two image locations. This task is further simplified if the object is positioned as an arrow standing upon the principal axis of the mirror. If this is the case, then the image will be standing upon the principal axis of the mirror (and either inverted or upright).

Of all the rays which emanate from the top of the object arrow and are incident to the mirror, there are two rays whose behavior at the mirror surface can be easily predicted. These are the two incident rays which are used in the ray construction. One of the rays moves parallel to the principal axis and reflects through the focal point. The second ray passes through the focal point on the way to the mirror and reflects parallel to the principal axis. All concave and convex mirror ray diagrams can be constructed from knowledge of the behavior of these two rays.

In the animation above, a right-side-up object is located above the principal axis at a position beyond the center of curvature (C). The ray diagram shows that the image of this object is located as an upside-down image positioned between the center of curvature (C) and the focal point (F). In fact, it can be generalized that anytime the object is located beyond the center of curvature, the image will be located somewhere between the center of curvature and the focal point. In such cases, the image will be inverted and reduced in size (i.e., smaller than the object). Such images are called real images because they are formed by the actual convergence of reflected light rays at the image location. Real images are always formed on the same side of the mirror as the object.

Object Located At the Center of Curvature

Ray diagrams are useful tools for determining the location of an image as produced by a concave mirror. To determine the location of an image using a ray diagram, at least two sets of incident and reflected rays must be constructed for strategic positions on the object. The image of an object is the location where light rays from that object intersect upon reflecting from a mirror. By constructing at least two sets of incident and reflected rays, this image location can easily be found.

If the object is represented by an arrow, then it is common practice to pick the two extreme positions (the top and the bottom of the arrow) as starting points for the incident and reflected rays. Ray construction will result in the determination of the image locations for these two extreme positions on the object. The complete image is merely an arrow connecting these two image locations. This task is further simplified if the object is positioned as an arrow standing upon the principal axis of the mirror. If this is the case, then the image will be standing upon the principal axis of the mirror (and either inverted or upright).

Of all the rays which emanate from the top of the object arrow and are incident to the mirror, there are two rays whose behavior at the mirror surface can be easily predicted. These are the two incident rays which are used in the ray construction. One of the rays moves parallel to the principal axis and reflects through the focal point. The second ray passes through the focal point on the way to the mirror and reflects parallel to the principal axis. All concave and convex mirror ray diagrams can be constructed from knowledge of the behavior of these two rays.

In the animation above, a right-side-up object is located above the principal axis at the center of curvature (C). The ray diagram shows that the image of this object is located as an upside-down image positioned at the center of curvature (C). In fact, it can be generalized that anytime the object is located at the center of curvature, the image will be located at the center of curvature as well. In such cases, the image will be inverted and the same size as the object. Such images are called real images because they are formed by the actual convergence of reflected light rays at the image location. Real images are always formed on the same side of the mirror as the object.

Object Located Between the Center of Curvature and the Focal Point

Ray diagrams are useful tools for determining the location of an image as produced by a concave mirror. To determine the location of an image using a ray diagram, at least two sets of incident and reflected rays must be constructed for strategic positions on the object. The image of an object is the location where light rays from that object intersect upon reflecting from a mirror. By constructing at least two sets of incident and reflected rays, this image location can easily be found.

If the object is represented by an arrow, then it is common practice to pick the two extreme positions (the top and the bottom of the arrow) as starting points for the incident and reflected rays. Ray construction will result in the determination of the image locations for these two extreme positions on the object. The complete image is merely an arrow connecting these two image locations. This task is further simplified if the object is positioned as an arrow standing upon the principal axis of the mirror. If this is the case, then the image will be standing upon the principal axis of the mirror (and either inverted or upright).

Of all the rays which emanate from the top of the object arrow and are incident to the mirror, there are two rays whose behavior at the mirror surface can be easily predicted. These are the two incident rays which are used in the ray construction. One of the rays moves parallel to the principal axis and reflects through the focal point. The second ray passes through the focal point on the way to the mirror and reflects parallel to the principal axis. All concave and convex mirror ray diagrams can be constructed from knowledge of the behavior of these two rays.


Object Located Between the Focal Point and the Mirror

Ray diagrams are useful tools for determining the location of an image as produced by a concave mirror. To determine the location of an image using a ray diagram, at least two sets of incident and reflected rays must be constructed for strategic positions on the object. The image of an object is the location where light rays from that object intersect upon reflecting from a mirror. By constructing at least two sets of incident and reflected rays, this image location can easily be found.

If the object is represented by an arrow, then it is common practice to pick the two extreme positions (the top and the bottom of the arrow) as starting points for the incident and reflected rays. Ray construction will result in the determination of the image locations for these two extreme positions on the object. The complete image is merely an arrow connecting these two image locations. This task is further simplified if the object is positioned as an arrow standing upon the principal axis of the mirror. If this is the case, then the image will be standing upon the principal axis of the mirror (and either inverted or upright).

Of all the rays which emanate from the top of the object arrow and are incident to the mirror, there are two rays whose behavior at the mirror surface can be easily predicted. These are the two incident rays which are used in the ray construction. One of the rays moves parallel to the principal axis and reflects through the focal point. The second ray passes through the focal point on the way to the mirror and reflects parallel to the principal axis. All concave and convex mirror ray diagrams can be constructed from knowledge of the behavior of these two rays.

In the animation above, a right-side-up object is located above the principal axis between the focal point (F) and the mirror. The ray diagram shows that the image of this object is located as a right-side up image positioned behind the mirror. In fact, it can be generalized that anytime the object is located between the focal point (F) and the mirror, the image will be located behind the mirror. In such cases, the image will be upright (not inverted) and larger in size than the object. Such images are called virtual images because they are not formed by the actual convergence of reflected light rays at the image location. Virtual images are always formed on the opposite side of the mirror as the object.