Magnification

The magnification of an optical instrument is the ratio between the apparent size ( size of the image ) and the true size of an object.

• In optical instruments with insight into an eyepiece under "size" of visual angle is to be understood ( viewing angle), this is called angular magnification.
• Does the picture on a screen is the "size" of a measure of length and can be measured with a ruler, then one speaks of linear magnification. The magnification in the direction transverse to the optical axis is called the lateral magnification, the magnification along the optical axis, which is crucial for the depth of field, ie Axialvergrößerung.

In all these cases, the magnification is a dimensionless number, which has no physical unit.

Angular magnification

The magnification (sometimes called ) of an optical instrument into which you look with the eye, is by definition:

Is the visual angle under which one sees an object G without optical aids ( drawn in black ). This angle depends on the distance between the eye and the object; The closer the object, the larger the visual angle. In magnifiers and microscopes therefore a distance of is assumed by convention, in which one could see the object without optical aids still sharp ( distinct vision ).

Is the viewing angle at which the object appears in the optical instrument (orange shown). The larger the visual angle, the greater the eye sees the object.

Magnifying glass

Formally, the magnification is calculated as follows:

Whereby 25 cm distance of distinct vision and corresponds to the object is located in the focal plane.

Microscope

The magnification of a microscope, the product of the magnification of the objective and the magnification of the eyepiece.

The magnification of the lens is calculated from

Wherein the focal length of the lens and the distance from the lens to the focal plane of the eyepiece is. Under the magnification of the lens is usually understood its image scale. With the magnification of a lens so no angular magnification is meant. It is assumed for the calculation that the lens is inserted, as is provided in the attached microscope. This means that the distance is chosen to subject such that the intermediate image is found where there is the focal plane of the eyepiece of the microscope (or newer microscopes, a CCD camera ). The distances of the two principal planes of the eyepiece to the object and the intermediate image are determined by the lens equation. In microscope systems with interchangeable lenses, the combination of the lenses is the microscope typically adjusted so that the optical tube length, so the distance between the eyepiece lens focal point and facing the intermediate image plane, for different lenses remains constant. This can easily calculate the magnification of the lens, that is, as

Usual is an optical tube length between.

The magnification of the eyepiece is like a magnifying glass by

Given. Just as the total magnification of a microscope it corresponds to an angular magnification.

Kepler telescope

The magnification of a telescope ( astronomical telescope or binoculars with inverting prisms ) is given by

Given. In this case, and the focal lengths of lens or eyepiece.

Also, the ratio of aperture ( lens diameter aperture) to the exit pupil of the telescope is given by the magnification. Since the eye can not capture more light than can pass through the pupil into the eye, it is a lower limit of magnification results (For a pupil diameter of the eye of 7 mm objective lens diameter in mm divided by 7). If this is exceeded, the light gathering power of the telescope is not fully utilized.

Since, due to the diffraction of light, the resolving power of the telescope is the lens diameter dependent, it is also an upper limit for the maximum useful magnification. The increase, which adjusts the resolution of the telescope to the human eye optimally is known as useful magnification. This is numerically about twice as large as the diameter of the telescope lens in millimeters. At a higher magnification stars appear not as points but as slices of the concentric circles ( diffraction rings ) are surrounded.

Limits of magnification

The magnification of an optical instrument is through the choice of lens and Okularbrennweiten further be increased, but the resolution is limited in optimal conditions by the diffraction of light, it is called diffraction-limited. If the magnification over the aperture of the instrument in millimeters, you can still see any smaller structures more, it is called dead magnification.

Under real conditions limit aberrations and with telescopes the turbulence of the air (" seeing " ) the maximum usable magnification even further. Although the recorded image can theoretically be increased arbitrarily strong, but the image information is limited. The picture is becoming increasingly blurred.