For a thin lens, the distances " S " 1 and " S " 2 are measured from the object and image to the position of the lens, as described above.
22.
By one, and likewise by several, and even by an infinite number of thin lenses in contact, no more than two axis points can be reproduced without aberration of the third order.
23.
Similarly to curved mirrors, thin lenses follow a simple equation that determines the location of the images given a particular focal length ( f ) and object distance ( S _ 1 ):
24.
They may be made of one or more conventional lenses or achromatic doublets, or a long cylindrical thin lens formula with object distance s = 2f, the image distance is calculated to s'= 2f ).
25.
For example, the condition for achromatism ( 4 ) for two thin lenses in contact is fulfilled in only one part of the spectrum, since dn _ 2 / dn _ 1 varies within the spectrum.
26.
:According to Lens ( optics ) # Compound lenses, the combined focal length of a pair of thin lenses of focal lengths f 1 and f 2 that are separated in air by a distance d is
27.
For the purposes of ray tracing, this is equivalent to a series of identical thin lenses of focal length " f " = " R " / 2, each separated from the next by length " d ".
28.
For two or more thin lenses close together, the optical power of the combined lenses is approximately equal to the sum of the optical powers of each lens : " P " = " P " 1 + " P " 2.
29.
In the limit of a " thin lens ", where the distances between the source, lens, and observer are much larger than the size of the lens ( this is almost always true for astronomical objects ), we can define the projected mass density
30.
If the distances from the object to the lens and from the lens to the image are " S " 1 and " S " 2 respectively, for a lens of negligible thickness, in air, the distances are related by the "'thin lens formula " ':
