Curved mirror

A concave mirror is a concave curved mirror ( concave mirror ). Practical use found mainly concave mirror in the form of a spherical section ( " spherical " mirrors) and in the form of paraboloids of revolution (see also: parabolic mirror ).

History

The French physician Pierre Borel, member of the Paris Academy of Sciences began in the 17th century the concave mirror as a research tool. For the purpose of medical examination and better illumination of body orifices, he constructed a concave mirror to reflect and focus the light onto the object to be examined. Concave mirrors are slightly modified still used as an end mirror or reflectors in medical diagnostics.

For earlier descriptions of the concave mirror, see the section in the article Archimedes burning mirror, Alhazen (especially the Alhazensche problem) and Treasure of optics (especially the fig of the title page ).

Two main variants

Analogous to the spherical and aspherical condenser lenses, there is also concave mirrors in two designs. The more complex and more expensive design has the advantage of substantially suppress the spherical aberration.

Parabolic mirror

Only the parabolic mirror, all light rays incident parallel to the optical axis, focused exactly at the focal point. The parabolic shape but is somewhat more complex than the spherical shape in the manufacturing process.

Spherical concave mirror

A parabolic mirror can be for small curvature angle approximated by a spherical surface, and with an accuracy which is sufficient for many applications. A spherical mirror is much easier to make than a parabolic mirror, so he often gets the preference.

The optical property of the concave mirror is determined by the radius of the sphere, the wall segment it is, the so-called curvature radius. If, in the center of the sphere an (imaginary ) point source of light, the mirror, the light source is reflected back to them. Come the light rays parallel from the infinite, so the mirror reflects it to focus ( focal point). This is about halfway between the center and mirror. The focal length of the concave mirror is thus half of its radius. However, the union of the rays of light occurs because of the spherical aberration there only imperfectly: the light beams form in the vicinity of the focus Catacaustic called a figure. (This is, however, avoided the parabolic mirror. )

Optical imaging

The considerations will be carried under the assumption that they take place in an angular region where spherical and parabolic mirrors behave about the same.

If you look inside the focal length, ie between the mirror and the focal point in a concave mirror, you see yourself enlarged, the image is upright and reversed, as in a plane mirror. Looking from outside the focal point in a concave mirror, the reflected image is upside down. The image produced by a concave mirror is the law of reflection predictable (see also: optical imaging ).

Concave mirrors are used among other things as the main mirror in reflecting telescopes, spectrometers and monochromators in optical as well as shaving. The satellite dishes for television reception or radar antennas work on the same principle, but for the light related radio waves.

Beam paths at different object distances

Similar to the convex lens produces a virtual image when the object distance is less than the focal length ( see inset ). A typical example is the mirror, which has only a slight curvature and thus a large focal length. The focal length is thus substantially greater than the distance of the viewer (which is in this case the object) to the mirror.

For object distances greater than the focal length is created, also similar to the convex lens, generally an inverted real image ( Exception: object distance equal to the focal length, see below). The magnification depends on the ratio of object distance from the focal length. An example here is the telescope mirror, in which the object distance is very large, and a greatly reduced image near the focal plane is created (so that a star on a photographic plate fits, it must be extremely reduced in size).

• Virtual ( behind the mirror )
• Upright

• The reflected rays of an image point are parallel - it creates a picture View Notes.

• Real
• Inverted

• Real
• Inverted
• Object and image are the same size

• Real
• Inverted
• Reduced
• In the limiting case in which the object distance tends to infinity at a great distance, the image is formed near or actually in the focal plane

Others; Trivia

In the magazine "Der Spiegel" there are on the penultimate page of a column called " concave mirror ". There, funny, curious and unintentionally funny newspaper clippings, newspaper headlines, advertisements, excerpts from manuals should be cited, and the like.