# Concave Spherical Mirrors

Concave mirrors have a curved surface with a center of curvature equidistant from every point on the mirror's surface. An object beyond the center of curvature forms a real and inverted image between the focal point and the center of curvature. This interactive tutorial explores how moving the object farther away from the center of curvature affects the size of the real image formed by the mirror. Also examined in the tutorial are the effects of moving the object closer to the mirror, first between the center of curvature and the focal point, and then between the focal point and the mirror surface (to form a virtual image).

The tutorial initializes with the object (an arrow) positioned with its tail in the center of the mirror's optical axis between the focal point and the mirror's center of curvature. To operate the tutorial, use the Object Position slider to translate the arrow back and forth in front of the mirror. As the arrow is moved away from the mirror, the inverted, real image grows larger and becomes equal in size to the object at the center of curvature. As the object is moved beyond the center of curvature, the image continues to grow smaller. Moving the object still closer to the mirror produces an even larger real image. When the object reaches the focal point, an upright, virtual image is produced on the rear side of the mirror and decreases in size as the object approaches the mirror surface.

The concave mirror has a reflection surface that curves inward, resembling a portion of the interior of a sphere. When light rays that are parallel to the principal or optical axis reflect from the surface of a concave mirror, they converge on the focal point (black dot) in front of the mirror. The distance from the reflecting surface to the focal point is known as the mirror's focal length. The size of the image depends upon the distance of the object from the mirror and its position with respect to the mirror surface. In this case, the if the object (the arrow) is placed just behind the center of curvature, then the reflected image is upside down and in front of the mirror's center of curvature.

The type of reflection that is seen in a mirror depends on its shape and, in some cases, how far away from the mirror the objects being reflected are positioned. Mirrors are not always flat and can be produced in a variety of configurations that provide interesting and useful reflection characteristics. Concave mirrors, commonly found in the largest optical telescopes, are used to collect the faint light emitted from very distant stars. The curved surface concentrates parallel rays from a great distance into a single point for enhanced intensity. This mirror design is also commonly found in shaving or cosmetic mirrors where the reflected light produces a magnified image of the face. The inside of a shiny spoon is a common example of a concave mirror surface, and can be used to demonstrate some properties of this mirror type. If the inside of the spoon is held close to the eye, a magnified upright view of the eye will be seen (in this case the eye is closer than the focal point of the mirror). If the spoon is moved farther away, a demagnified upside-down view of the whole face will be seen.

#### Contributing Authors

Matthew J. Parry-Hill, Thomas J. Fellers and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.