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Magnification is the process of enlarging the , not physical size, of something. 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
visual The visual system comprises the sensory organ (the eye) and parts of the central nervous system (the retina containing photoreceptor cells, the optic nerve The optic nerve, also known as cranial nerve II, or simply as CN II, is a paired ...
s or
image An SAR radar imaging, radar image acquired by the SIR-C/X-SAR radar on board the Space Shuttle Endeavour shows the Teide volcano. The city of Santa Cruz de Tenerife is visible as the purple and white area on the lower right edge of the island ...

s to be able to see more detail, increasing resolution, using
microscope A microscope (from the grc, μικρός, ''mikrós'', "small" and , ''skopeîn'', "to look" or "see") is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science Scie ...
,
printing Printing is a process for mass reproducing text and images using a master form or template. The earliest non-paper products involving printing include cylinder seals and objects such as the Cyrus Cylinder and the Cylinders of Nabonidus. The ...
techniques, or digital processing. In all cases, the magnification of the image does not change the perspective of the image.

# Examples of magnification

Some optical instruments provide visual aid by magnifying small or distant subjects. * A
magnifying glass A magnifying glass (called a hand lens in laboratory contexts) is a Lens (optics)#Types of simple lenses, convex lens that is used to produce a magnification, magnified image of an object. The lens (optics), lens is usually mounted in a frame with ...
, which uses a positive (convex) lens to make things look bigger by allowing the user to hold them closer to their eye. * A
telescope A telescope is an optical instrument using lenses, curved mirrors, or a combination of both to observe distant objects, or various devices used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation ...
, which uses its large objective lens or primary mirror to create an image of a distant object and then allows the user to examine the image closely with a smaller
eyepiece An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is so named because it is usually the lens that is closest to the eye when someone looks through the device. ...
lens, thus making the object look larger. * A
microscope A microscope (from the grc, μικρός, ''mikrós'', "small" and , ''skopeîn'', "to look" or "see") is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science Scie ...
, which makes a small object appear as a much larger image at a comfortable distance for viewing. A microscope is similar in layout to a telescope except that the object being viewed is close to the objective, which is usually much smaller than the eyepiece. * A slide projector, which projects a large image of a small slide on a screen. A photographic
enlarger An enlarger is a specialized transparency projector used to produce photographic prints from film or glass negatives, or from transparencies. Construction All enlargers consist of a light source, normally an incandescent light bulb shining tho ...
is similar.

# 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 In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the SI of the ...
. Optical magnification is sometimes referred to as "power" (for example "10× power"), although this can lead to confusion with
optical power Optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror Grange, East Yorkshire, UK, from World War I. The mirror magnified the sound of approaching ene ...
.

## Linear or Transverse magnification

For s, such as images projected on a screen, ''size'' means a linear dimension (measured, for example, in millimeters or inches).

## Angular magnification

For optical instruments with an
eyepiece An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is so named because it is usually the lens that is closest to the eye when someone looks through the device. ...
, the linear dimension of the image seen in the eyepiece (virtual image in infinite distance) cannot be given, thus ''size'' means the angle subtended by the object at the focal point (angular size). Strictly speaking, one should take the tangent of that angle (in practice, this makes a difference only if the angle is larger than a few degrees). Thus, angular magnification is given by: $\mathrm=\frac$ 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. For example, the mean angular size of the Moon's disk as viewed from Earth's surface is about 0.52°. Thus, through binoculars with 10× magnification, the Moon appears to subtend an angle of about 5.2°. By convention, for
magnifying glass A magnifying glass (called a hand lens in laboratory contexts) is a Lens (optics)#Types of simple lenses, convex lens that is used to produce a magnification, magnified image of an object. The lens (optics), lens is usually mounted in a frame with ...
es and optical
microscope A microscope (from the grc, μικρός, ''mikrós'', "small" and , ''skopeîn'', "to look" or "see") is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science Scie ...
s, 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.

## By instrument

### Single lens

The linear magnification of a thin lens is $M =$ where $f$ is the focal length and $d_o$ is the distance from the lens to the object. Note that for s, $M$ is negative and the image is inverted. For virtual images, $M$ is positive and the image is upright. With $d_i$ being the distance from the lens to the image, $h_i$ the height of the image and $h_o$ the height of the object, the magnification can also be written as: $M = - =$ Note again that a negative magnification implies an inverted image.

### Photography

The image recorded by a photographic film or image sensor is always a and is usually inverted. When measuring the height of an inverted image using the Cartesian coordinate system, cartesian sign convention (where the x-axis is the optical axis) the value for ''hi'' will be negative, and as a result ''M'' will also be negative. However, the traditional sign convention used in photography is "real image, real is positive, virtual image, virtual is negative". Therefore, in photography: Object height and distance are always ''real'' and positive. When the focal length is positive the image's height, distance and magnification are ''real'' and positive. Only if the focal length is negative, the image's height, distance and magnification are ''virtual'' and negative. Therefore, the ''photographic magnification'' formulae are traditionally presented as $M = = = =$

### Telescope

The angular magnification of an optical telescope is given by $M=$ in which $f_o$ is the focal length of the objective (optics), objective lens (optics), lens in a refracting telescope, refractor or of the primary mirror in a reflecting telescope, reflector, and $f_e$ is the focal length of the
eyepiece An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is so named because it is usually the lens that is closest to the eye when someone looks through the device. ...
.

### Magnifying glass

The maximum angular magnification (compared to the naked eye) of a
magnifying glass A magnifying glass (called a hand lens in laboratory contexts) is a Lens (optics)#Types of simple lenses, convex lens that is used to produce a magnification, magnified image of an object. The lens (optics), lens is usually mounted in a frame with ...
depends on how the glass and the object are held, relative to the eye. If the lens is held at a distance from the object such that its front focal point is on the object being viewed, the relaxed eye (focused to infinity) can view the image with angular magnification $\mathrm=\quad$ Here, $f$ is the focal length of the lens (optics), lens in centimeters. The constant 25 cm is an estimate of the "near point" distance of the eye—the 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 $\mathrm=+1\quad$ 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.

### Microscope

The angular magnification of a
microscope A microscope (from the grc, μικρός, ''mikrós'', "small" and , ''skopeîn'', "to look" or "see") is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science Scie ...
is given by $\mathrm=M_o \times M_e$ where $M_o$ is the magnification of the objective and $M_e$ the magnification of the eyepiece. The magnification of the objective depends on its focal length $f_o$ and on the distance $d$ between objective back focal plane and the focal plane of the
eyepiece An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is so named because it is usually the lens that is closest to the eye when someone looks through the device. ...
(called the tube length): $M_o=$ The magnification of the eyepiece depends upon its focal length $f_e$ 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 Plus and minus signs, 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 :$\mathrm =1 / M = D_/$.

## 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-limited system, 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 Optical microscope#Limitations, 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.