= Optical power
{title2=$\Phi=1/f$}
{wiki}
The <optical power> is reciprocal signed <focal length>, $\Phi=1/f$. With $f$ expressed in metres, <optical power> is expressed in <dioptres>: $f=1\,\mathrm m$ gives $\Phi=+1\,\mathrm D$, while $f=-0.5\,\mathrm m$ gives $\Phi=-2\,\mathrm D$. The sign distinguishes converging and diverging <optical lens> elements; the magnitude measures how strongly they change the direction of a <light ray> at a given height. https://openstax.org/books/college-physics-2e/pages/25-6-image-formation-by-lenses[Urone and Hinrichs, OpenStax College Physics 2e, §25.6: Optical power and diopters]{ref}.
For two ideal <thin lens> elements in contact in air, <optical powers> add: $\Phi_{\rm total}=\Phi_1+\Phi_2$. Thus $+2\,\mathrm D$ and $-1\,\mathrm D$ combine to give $+1\,\mathrm D$, or $f_{\rm total}=1\,\mathrm m$. Separation changes the rule: for two ideal <thin lens> elements separated by $d$ in air, their equivalent <optical power> is $\Phi_1+\Phi_2-d\Phi_1\Phi_2$. The contact rule is the $d=0$ case.<MIT 2.71 and 2.710 Optics, Spring 2014 by Nicholas X. Fang/Lecture Notes on Geometrical Optics>[§J: Composite lenses]{ref}
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