Editing Magnification (section)

===Single lens===
The linear magnification of a [[thin lens]] is

<math display="block">M = {f \over f-d_\mathrm{o}} = - \frac{f}{x_o}</math>

where <math display="inline">f</math> is the [[focal length]], <math display="inline">d_\mathrm{o}</math> is the distance from the lens to the object, and <math display="inline">x_0 = d_0 - f</math> as the distance of the object with respect to the front focal point. A [[Lens#Sign convention for other parameters|sign convention]] is used such that <math display="inline">d_0</math> and <math>d_i</math> (the image distance from the lens) are positive for real object and image, respectively, and negative for virtual object and images, respectively. <math display="inline">f</math> of a converging lens is positive while for a diverging lens it is negative.

For [[real image]]s, <math display="inline">M</math> is negative and the image is inverted. For [[virtual image]]s, <math display="inline">M</math> is positive and the image is upright.

With <math display="inline">d_\mathrm{i}</math> being the distance from the lens to the image, <math display="inline">h_\mathrm{i}</math> the height of the image and <math display="inline">h_\mathrm{o}</math> the height of the object, the magnification can also be written as:

<math display="block">M = -{d_\mathrm{i} \over d_\mathrm{o}} = {h_\mathrm{i} \over h_\mathrm{o}}</math>

Note again that a negative magnification implies an inverted image.

The image magnification along the optical axis direction <math>M_L</math>, called longitudinal magnification, can also be defined. [[Lens#Lens equation|The Newtonian lens equation]] is stated as <math>f^2 = x_0 x_i</math>, where <math display="inline">x_0 = d_0 - f</math> and <math display="inline">x_i = d_i - f</math> as on-axis distances of an object and the image with respect to respective focal points, respectively. <math>M_L</math> is defined as 

<math display="block">M_L = \frac{dx_i}{dx_0},</math>

and by using the Newtonian lens equation, 

<math display="block">M_L = - \frac{f^2}{x_o^2} = - M^2.</math>

The longitudinal magnification is always negative, means that, the object and the image move toward the same direction along the optical axis. The longitudinal magnification varies much faster than the transverse magnification, so the 3-dimensional image is distorted.