Editing Chromatic aberration (section)

===Mathematics of chromatic aberration minimization===

For a doublet consisting of two thin lenses in contact, the [[Abbe number]] of the lens materials is used to calculate the correct focal length of the lenses to ensure correction of chromatic aberration.<ref>Sacek, Vladmir. [http://www.telescope-optics.net/designing_doublet_achromat.htm "9.3. DESIGNING DOUBLET ACHROMAT."] telescope-optics.net</ref> If the focal lengths of the two lenses for light at the yellow [[Fraunhofer lines|Fraunhofer]] D-line (589.2&nbsp;nm) are ''f''<sub>1</sub> and ''f''<sub>2</sub>, then best correction occurs for the condition:
:<math>f_1 \cdot V_1 + f_2 \cdot V_2 = 0</math>
where ''V''<sub>1</sub> and ''V''<sub>2</sub> are the Abbe numbers of the materials of the first and second lenses, respectively. Since Abbe numbers are positive, one of the focal lengths must be negative, i.e., a diverging lens, for the condition to be met.

The overall focal length of the doublet ''f'' is given by the standard formula for thin lenses in contact:
:<math>\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}</math>
and the above condition ensures this will be the focal length of the doublet for light at the blue and red Fraunhofer F and C lines (486.1&nbsp;nm and 656.3&nbsp;nm respectively). The focal length for light at other visible wavelengths will be similar but not exactly equal to this.

Chromatic aberration is used during a [[duochrome test|duochrome eye test]] to ensure that a correct lens power has been selected. The patient is confronted with red and green images and asked which is sharper. If the prescription is right, then the cornea, lens and prescribed lens will focus the red and green wavelengths just in front, and behind the retina, appearing of equal sharpness. If the lens is too powerful or weak, then one will focus on the retina, and the other will be much more blurred in comparison.<ref>{{Cite journal
 | pmid = 1469739
| year = 1992
| last1 = Colligon-Bradley
| first1 = P
| title = Red-green duochrome test
| journal = Journal of Ophthalmic Nursing & Technology
| volume = 11
| issue = 5
| pages = 220–2
}}</ref>