For other uses, see Magnification (disambiguation).
The stamp appears larger with the use of a magnifying glass
Stepwise magnification by 6% per frame into a 39 megapixel image. In the final frame, at about 170x, an image of a bystander is seen reflected in the man's cornea

'Magnification is the process of enlarging something only in appearance, not in physical size. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in size, sometimes called "minification" or "de-magnification".

Typically, magnification is related to scaling up visuals or images to be able to see more detail, increasing resolution, using microscope, printing techniques, or digital processing. In all cases, the magnification of the image does not change the perspective of the image.

Examples of magnification

Magnification as a number (optical magnification)

Optical magnification is the ratio between the apparent size of an object (or its size in an image) and its true size, and thus it is a dimensionless number.

where is the angle subtended by the object at the front focal point of the objective and is the angle subtended by the image at the rear focal point of the eyepiece.
  • Example: The angular size of the full moon is 0.5°. In binoculars with 10x magnification it appears to subtend an angle of 5°.
By convention, for magnifying glasses and optical microscopes, where the size of the object is a linear dimension and the apparent size is an angle, the magnification is the ratio between the apparent (angular) size as seen in the eyepiece and the angular size of the object when placed at the conventional closest distance of distinct vision: 25 cm from the eye.

Optical magnification is sometimes referred to as "power" (for example "10× power"), although this can lead to confusion with optical power.

A Thin lens where black dimensions are real, grey are virtual. The direction of the arrows can be used to describe cartesian +/- signage : from the centre of the lens, left or down = negative, right or up = positive.
where is the focal length and is the distance from the lens to the object. Note that for real images, is negative and the image is inverted. For virtual images, is positive and the image is upright.
With being the distance from the lens to the image, the height of the image and the height of the object, the magnification can also be written as:
Note again that a negative magnification implies an inverted image.
where is the focal length of the objective lens and is the focal length of the eyepiece.
Here, is the focal length of the lens in centimeters. The constant 25 cm is an estimate of the "near point" distance of the eyethe closest distance at which the healthy naked eye can focus. In this case the angular magnification is independent from the distance kept between the eye and the magnifying glass.
If instead the lens is held very close to the eye and the object is placed closer to the lens than its focal point so that the observer focuses on the near point, a larger angular magnification can be obtained, approaching
A different interpretation of the working of the latter case is that the magnifying glass changes the diopter of the eye (making it myopic) so that the object can be placed closer to the eye resulting in a larger angular magnification.
where is the magnification of the objective and the magnification of the eyepiece. The magnification of the objective depends on its focal length and on the distance between objective back focal plane and the focal plane of the eyepiece (called the tube length):
The magnification of the eyepiece depends upon its focal length and is calculated by the same equation as that of a magnifying glass (above).

Note that both astronomical telescopes as well as simple microscopes produce an inverted image, thus the equation for the magnification of a telescope or microscope is often given with a minus sign.

Measurement of telescope magnification

Measuring the actual angular magnification of a telescope is difficult, but it is possible to use the reciprocal relationship between the linear magnification and the angular magnification, since the linear magnification is constant for all objects.

The telescope is focused correctly for viewing objects at the distance for which the angular magnification is to be determined and then the object glass is used as an object the image of which is known as the exit pupil. The diameter of this may be measured using an instrument known as a Ramsden dynameter which consists of a Ramsden eyepiece with micrometer hairs in the back focal plane. This is mounted in front of the telescope eyepiece and used to evaluate the diameter of the exit pupil. This will be much smaller than the object glass diameter, which gives the linear magnification (actually a reduction), the angular magnification can be determined from


Maximum usable magnification

With any telescope or microscope,or a lens a maximum magnification exists beyond which the image looks bigger but shows no more detail. It occurs when the finest detail the instrument can resolve is magnified to match the finest detail the eye can see. Magnification beyond this maximum is sometimes called "empty magnification".

For a good quality telescope operating in good atmospheric conditions, the maximum usable magnification is limited by diffraction. In practice it is considered to be 2× the aperture in millimetres or 50× the aperture in inches; so, a 60mm diameter telescope has a maximum usable magnification of 120×.

With an optical microscope having a high numerical aperture and using oil immersion, the best possible resolution is 200 nm corresponding to a magnification of around 1200×. Without oil immersion, the maximum usable magnification is around 800×. For details, see limitations of optical microscopes.

Small, cheap telescopes and microscopes are sometimes supplied with the eyepieces that give magnification far higher than is usable.

Magnification and micron bar

Magnification figures on printed pictures can be misleading. Editors of journals and magazines routinely resize images to fit the page, making any magnification number provided in the figure legend incorrect. A scale bar (or micron bar) is a bar of stated length superimposed on a picture. This bar can be used to make accurate measurements on a picture. When a picture is resized the bar will be resized in proportion. If a picture has a scale bar, the actual magnification can easily be calculated. Where the scale (magnification) of an image is important or relevant, including a scale bar is preferable to stating magnification.

See also

Look up magnification in Wiktionary, the free dictionary.


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