For: Magnification (album)

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

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.

• 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 optical instruments with an eyepiece, 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 defined as

  $\backslash mathrm\{MA\}=\backslash frac\{\backslash tan\; \backslash varepsilon\}\{\backslash tan\; \backslash varepsilon\_0\}$,

  where $\{\backslash varepsilon\_0\}$ is the angle subtended by the object at the front focal point of the objective and $\{\backslash varepsilon\}$ 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°, which is roughly 1/10th of the field of view of typical eyepieces.

  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 of 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.

  Calculating the magnification of optical systems

  • Single lens: The linear magnification of a thin lens is

    $M\; =\; \{f\; \backslash over\; f-d\_o\}$

    where $f$ is the focal length and $d\_o$ is the distance from the lens to the object. Note that for real images, $M$ 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:

    $M\; =\; -\{d\_i\; \backslash over\; d\_o\}\; =\; \{h\_i\; \backslash over\; h\_o\}$