## Abstract

The horizontal foci of a Tandem Wadsworth spectrograph are calculated by using the correct ruling densities for both gratings. Results are quite different from those of previous analyses that used approximate ruling densities. Ray tracings confirm the analyses with the correct ruling densities and also indicate that this spectrograph possesses the excellent, nearly stigmatic properties found by the approximate analyses.

© 1979 Optical Society of America

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### Equations (6)

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(1)
$$tan{\alpha}_{1}=\frac{sin{\theta}_{1}}{1-cos{\theta}_{1}+1/cos{\beta}_{s}}.$$
(2)
$$sin{\beta}_{1}=(m\mathrm{\lambda}/{\sigma}_{0})cos{\theta}_{1}-sin{\alpha}_{1}.$$
(3)
$${\theta}_{2}=2{\beta}_{1}-2{\beta}_{s}+{\theta}_{1}.$$
(4)
$$sin{\beta}_{2}=(m\mathrm{\lambda}/{\sigma}_{0})cos{\theta}_{2}-sin{\alpha}_{2}.$$
(5)
$$\begin{array}{ll}{r}_{2h}^{\prime}({\theta}_{1}\to 0)\hfill & =R-{({X}^{2}+{R}^{2}-2XRcos{\beta}_{2})}^{1/2}\hfill \\ \hfill X& =Rcos{\beta}_{2}{\left[1+\frac{1}{cos{\beta}_{2}}\left(\frac{m\mathrm{\lambda}}{{\sigma}_{0}}sin2({\beta}_{1}-{\beta}_{s})+\frac{cos{\beta}_{1}cos{\beta}_{s}}{2cos{\beta}_{s}-cos{\beta}_{1}}\right)\right]}^{-1}.\hfill \end{array}$$
(6)
$${r}_{2h}^{\prime}({\theta}_{1})={r}_{2h}^{\prime}({\theta}_{1}\to 0)-0.0115{\theta}_{1}^{2}$$