= Chromatic aberration
{wiki}
An <optical camera> can focus a white object sharply in one colour while leaving coloured fringes around its edges in another. <Chromatic aberration> is the dependence of image position or image scale on <wavelength>, caused by <optical dispersion> in the <optical lens> materials. <Axial chromatic aberration> separates the <optical foci> along the <optical axis>; <lateral chromatic aberration> changes the <transverse magnification> with <wavelength>. Moving the receiving plane can favour one colour without bringing all colours into focus. https://farside.ph.utexas.edu/teaching/302l/lectures/node142.html[Richard Fitzpatrick, University of Texas at Austin, Chromatic aberration]{ref}; https://imaging.nikon.com/sport-optics/guide/fieldscopes/choosing/choosing_03/[Nikon, Comparison of ED glass and ordinary lens]{ref}.
For ordinary <optical glass> in the visible range, the blue <refractive index> exceeds the red <refractive index>. For a fixed positive <thin lens> in air, the <lensmaker's equation> then gives
$$
\Phi(\lambda)=\frac{1}{f(\lambda)}=[n(\lambda)-1]\left(\frac{1}{R_a}-\frac{1}{R_b}\right),\qquad n_{\rm blue}>n_{\rm red}\ \Longrightarrow\ \Phi_{\rm blue}>\Phi_{\rm red}>0,\quad f_{\rm blue}<f_{\rm red}.
$$
Here $\lambda$ is <wavelength>, $n$ is <refractive index>, $\Phi$ is <optical power>, $f$ is <focal length>, and $R_a,R_b$ are the signed surface <radius of curvature> values in the <lensmaker's equation>. The blue <light rays> therefore bend more strongly and meet sooner. This ordering is a statement about ordinary visible <optical dispersion>, not a universal rule for every material and every spectral range. https://farside.ph.utexas.edu/teaching/302l/lectures/node142.html[Fitzpatrick, Chromatic aberration, colour-dependent focusing]{ref}.
For a worked example, take a single positive <thin lens> with reference <optical power> $\Phi_d=5\,\mathrm D$ and <Abbe number> $V_d=60$, hence reference <focal length> $f_d=0.2\,\mathrm m$. Its F–C <optical power> difference is $\Delta\Phi=\Phi_F-\Phi_C=\Phi_d/V_d=5/60\,\mathrm D\approx0.08333\,\mathrm D$, by the <achromatic doublet power balance> relation below. This difference alone does not locate the reference <optical power> within the F–C interval. To draw a transparent example, introduce a synthetic colour coordinate $q$, a <dimensionless quantity>, with red $q=-1/2$, reference $q=0$, and blue $q=+1/2$, and choose the toy <optical dispersion> model
$$
\Phi(q)=\Phi_d\left(1+\frac{q}{V_d}\right),\qquad f(q)=\frac{1}{\Phi(q)}.
$$
The diagram's red and blue endpoints represent the C and F endpoints of this toy model. Its reference point is placed symmetrically in <optical power> by construction; $q$ is not a measured <wavelength> scale, and the model is not measured <optical glass> data. The endpoint <focal lengths> are
$$
f_{\rm red}=\frac{1}{5(1-1/120)}\,\mathrm m=\frac{24}{119}\,\mathrm m\approx0.201681\,\mathrm m,\qquad f_{\rm blue}=\frac{1}{5(1+1/120)}\,\mathrm m=\frac{24}{121}\,\mathrm m\approx0.198347\,\mathrm m.
$$
Thus the <axial chromatic aberration> in this example separates the endpoint <optical foci> by about $3.334\,\mathrm{mm}$. A single receiving plane cannot coincide with both <optical foci>.
\Image[/chromatic-aberration-focal-split.png]
{title=<Chromatic aberration>: the blue <optical focus> precedes the red <optical focus> in a toy single <thin lens>}
{description=Parallel incoming <light rays> meet an ideal positive <thin lens> at $x=0$. The right panel enlarges the neighbourhood of the three <optical foci>; the reference <focal length> is $200\,\mathrm{mm}$. The synthetic model uses $\Phi_d=5\,\mathrm D$, $V_d=60$, and $q=-1/2,0,+1/2$. This is toy <optical dispersion>, not measured <optical glass>; the vertical scales are enlarged.}
The useful design idea is to cancel changes of <optical power> while retaining a positive total <optical power>. An <achromatic lens> does this with materials having different <Abbe numbers>. It greatly reduces <chromatic aberration>, but correcting two chosen <wavelengths> still leaves the possibility of a <secondary spectrum>.
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