Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a size ratio called optical magnification. When this number is less than one, it refers to a reduction in size, sometimes called 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 Some optical instruments provide visual aid by magnifying small or distant subjects.
A magnifying glass, which uses a positive (convex) lens to make things look bigger by allowing the user to hold them closer to their eye. A telescope, 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 lens, thus making the object look larger. A microscope, 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 is similar. A zoom lens, a system of camera lens elements for which the focal length and angle of view can be varied.
Size ratio (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. Optical magnification is sometimes referred to as "power" (for example "10× power"), although this can lead to confusion with optical power.
Linear or transverse magnification For real images, such as images projected on a screen, size means a linear dimension (measured, for example, in millimeters or inches).
Angular magnification For an optical instrument with an eyepiece as an example, the linear dimension of an image seen through the eyepiece cannot be given if it is an virtual image at an infinite distance, thus size in this case may mean the angle subtended between an edge (or both edges, depending on the definition) of the image and the optical axis of the instrument (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
M A = tan ε tan ε 0 ≈ ε ε 0 {\displaystyle M_{A}={\frac {\tan \varepsilon }{\tan \varepsilon _{0}}}\approx {\frac {\varepsilon }{\varepsilon _{0}}}}
where ε 0 {\textstyle \varepsilon _{0}} is the angle subtended by an object (w.r.t the optical axis) and ε {\textstyle \varepsilon } is the angle subtended by its image (also w.r.t the optical axis) made by an optical instrument. 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 glasses and optical microscopes, where the size of an object is a linear dimension and the apparent size (the image size) of it is an angle, the magnification is the ratio between the apparent (angular) size as seen via instrument and the angular size of the object when the object is placed at the conventional closest distance of distinct vision to an unaided human eye: 25 cm from the eye (called the near point).
By instrument
Single lens The linear magnification of a thin lens is
M = f f − d o = − f x o {\displaystyle M={f \over f-d_{\mathrm {o} }}=-{\frac {f}{x_{o}}}}
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