Editing Lens (section)

=== Magnification ===
The linear ''[[magnification]]'' of an imaging system using a single lens is given by

<math display="block"> M = - \frac{S_2}{S_1} = \frac{f}{f - S_1}\ = - \frac{f}{x_1}</math>
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where {{mvar|M}} is the magnification factor defined as the ratio of the size of an image compared to the size of the object. The sign convention here dictates that if {{mvar|M}} is negative, as it is for real images, the image is upside-down with respect to the object. For virtual images {{mvar|M}} is positive, so the image is upright.

This magnification formula provides two easy ways to distinguish converging ({{math|''f'' > 0}}) and diverging ({{math|''f'' < 0}}) lenses: For an object very close to the lens ({{math|1=0 < ''S''{{sub|1}} < {{abs|''f''}}}}), a converging lens would form a magnified (bigger) virtual image, whereas a diverging lens would form a demagnified (smaller) image; For an object very far from the lens ({{math|1=''S''{{sub|1}} > {{abs|''f''}} > 0}}), a converging lens would form an inverted image, whereas a diverging lens would form an upright image.

Linear magnification {{mvar|M}} is not always the most useful measure of magnifying power. For instance, when characterizing a visual telescope or binoculars that produce only a virtual image, one would be more concerned with the [[Magnification#Angular magnification|angular magnification]]—which expresses how much larger a distant object appears through the telescope compared to the naked eye. In the case of a camera one would quote the [[plate scale]], which compares the apparent (angular) size of a distant object to the size of the real image produced at the focus. The plate scale is the reciprocal of the focal length of the camera lens; lenses are categorized as [[long-focus lens]]es or [[wide-angle lens]]es according to their focal lengths.

Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. For instance, using a magnifying glass of {{val|5|u=cm}} focal length, held {{val|20|u=cm}} from the eye and {{val|5|u=cm}} from the object, produces a virtual image at infinity of infinite linear size: {{math|1=''M'' = ∞}}. But the ''{{dfn|angular magnification}}'' is 5, meaning that the object appears 5 times larger to the eye than without the lens. When taking a picture of the [[moon]] using a camera with a {{val|50|u=mm}} lens, one is not concerned with the linear magnification {{math|1=''M'' ≈ {{val|-50|u=mm}} / {{val|380000|u=km}} = {{val|-1.3|e=-10}}.}} Rather, the plate scale of the camera is about {{val|1|u=°|up=mm}}, from which one can conclude that the {{val|0.5|u=mm}} image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.

In the extreme case where an object is an infinite distance away, {{math|1=''S''{{sub|1}} = ∞}}, {{math|1=''S''{{sub|2}} = ''f''}} and {{math|1=''M'' = −''f''/∞ = 0}}, indicating that the object would be imaged to a single point in the focal plane. In fact, the diameter of the projected spot is not actually zero, since [[diffraction]] places a lower limit on the size of the [[point spread function]]. This is called the [[diffraction limit]].

[[File:Thin lens images.svg|thumb|Images of black letters in a thin convex lens of focal length {{mvar|f}} are shown in red. Selected rays are shown for letters '''E''', '''I''' and '''K''' in blue, green and orange, respectively. '''E''' (at {{math|2''f''}}) has an equal-size, real and inverted image; '''I''' (at {{mvar|f}}) has its image at [[infinity]]; and '''K''' (at {{math|''f''/2}}) has a double-size, virtual and upright image.

Note that the images of letters H, I, J, and i are located far away from the lens such that they are not shown here. What is also shown here that the ray that is parallelly incident on the lens and refracted toward the second focal point ''f'' determines the image size while other rays help to locate the image location.]]