## Abstract

Equations are given for the condition that the focal surface of a lens system remain at a predetermined position for a range of ambient temperatures. Simple methods of satisfying these equations for lens systems composed predominantly or entirely of plastic components are described.

© 1948 Optical Society of America

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### Equations (11)

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(1)
$$(1/S)+(1/{S}^{\prime})=(n-1)[(1/{R}_{a})-(1/{R}_{b})].$$
(2)
$$({D}_{T}S/{S}^{2})+({D}_{T}{S}^{\prime}/{({S}^{\prime})}^{2})=-[(1/{R}_{a})-(1/{R}_{b})]{D}_{T}n+[({D}_{T}{R}_{a}/{{R}_{a}}^{2})-({D}_{T}{R}_{b}/{{R}_{b}}^{2})](n+1).$$
(3)
$$({D}_{T}S/{S}^{2})+({D}_{T}{S}^{\prime}/{({S}^{\prime})}^{2})=(1/f)[-({D}_{T}n/(n-1))+{E}_{T}].$$
(4)
$$({D}_{T}S/{S}^{2})+({D}_{T}{S}^{\prime}/{({S}^{\prime})}^{2})=-1/f{\nu}_{T},$$
(5)
$${D}_{T}{{S}_{N}}^{\prime}=-\sum _{k=1}^{k=N}{({h}^{2}/f{\nu}_{T})}_{k},$$
(6)
$$F(n)=[[({n}^{2}+2)(n+1)/2n]+1].$$
(7)
$$\begin{array}{l}{D}_{T}{{S}_{N}}^{\prime}=-({D}_{T}{S}_{1}/{{S}_{1}}^{2})\\ -\sum _{k=1}^{k=N}\mathbf{[}[({\varphi}_{a}{{h}_{a}}^{2}+{\varphi}_{b}{{h}_{b}}^{2})/{\nu}_{T}]\\ +{({h}_{a}/{{S}_{a}}^{\prime})}^{2}{n}^{2}{D}_{T}(t/n)\\ +{({h}_{b}/{{S}_{b}}^{\prime})}^{2}{D}_{T}L{\mathbf{]}}_{k},\end{array}$$
(8)
$$\begin{array}{l}{D}_{T}{{S}_{N}}^{\prime}/{{n}_{0}}^{\prime}=({{S}_{N}}^{\prime}/{({{n}_{0}}^{\prime})}^{2}){D}_{T}({{n}_{0}}^{\prime})\\ -[({n}_{0}{D}_{T}{S}_{1}-{S}_{1}{D}_{T}{n}_{0})/{{S}_{1}}^{2}]\\ -\sum _{k=1}^{k=N}\mathbf{[}[({\varphi}_{a}{{h}_{a}}^{2}+{\varphi}_{b}{{h}_{b}}^{2})/{\nu}_{T}]\\ +{({h}_{a}/{{S}_{a}}^{\prime})}^{2}{n}^{2}{D}_{T}(t/n)\\ +{({h}_{b}/{{S}_{b}}^{\prime})}^{2}{D}_{T}L{\mathbf{]}}_{k}.\end{array}$$
(9)
$${[{({h}_{a}/{{S}_{a}}^{\prime})}^{2}{n}^{2}{D}_{T}(t/n)]}_{k}$$
(10)
$${({h}_{a}/{{S}_{a}}^{\prime})}^{2}{n}^{2}{D}_{T}(t/n)$$
(11)
$${{h}_{k}}^{2}{[-{(2/R)}^{2}{E}_{T}+{(1/{S}^{\prime})}^{2}{D}_{T}L]}_{k}.$$