## Abstract

A method is outlined by which the limiting resolving power of any prism may be readily determined. It has been necessary to redefine the limit of resolution as the minimum angular of the central maxima of the individual diffraction images at which there may exist a minimum of total intensity between the positions of the individual central maxima. Application to a 10-cm rocksalt prism is included.

© 1944 Optical Society of America

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### Equations (17)

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(1)
$$I({\theta}_{0}+d\theta )+I({\theta}_{0}-d\theta )\u2a7e2I({\theta}_{0}).$$
(2)
$${({d}^{2}I/d{\theta}^{2})}_{{\theta}_{0}}\u2a7e0.$$
(4)
$$dI/d\theta =K(2w{e}^{-fw}Z\hspace{0.17em}\text{sin}\hspace{0.17em}w\theta -2\theta E)/{Z}^{2},$$
(5)
$${d}^{2}I/d{\theta}^{2}=K[2{w}^{2}{e}^{-fw}{Z}^{2}\hspace{0.17em}\text{cos}\hspace{0.17em}w\theta +8{\theta}^{2}E-2Z(4w\theta {e}^{-fw}\hspace{0.17em}\text{sin}\hspace{0.17em}w\theta +E)]/{Z}^{3}.$$
(6)
$$\begin{array}{l}\{(2+{f}^{2}{w}^{2})+{r}^{2}[{r}^{2}{f}^{2}{w}^{2}+(2{f}^{2}{w}^{2}-6)]\}\hspace{0.17em}\text{cos}\hspace{0.17em}rfw\\ -4rfw(1+{r}^{2})\hspace{0.17em}\text{sin}\hspace{0.17em}rfw+(6{r}^{2}-2)\hspace{0.17em}\text{cosh}\hspace{0.17em}fw=0.\end{array}$$
(7)
$$\underset{fw\to 0}{\text{Lim}}\hspace{0.17em}rfw=2.606\cdots ,$$
(8)
$$\underset{fw\to \infty}{\text{Lim}}\hspace{0.17em}rfw={3}^{-{\scriptstyle \frac{1}{2}}}fw.$$
(9)
$$\mathrm{\Delta}D=\mathrm{\lambda}kM/2\xb7{3}^{{\scriptstyle \frac{1}{2}}}\pi W=\mathrm{\lambda}kM/10.883W.$$
(10)
$$0<kM<1:\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\text{L.R.P.}=1.2W(dD/dn)(dn/d\mathrm{\lambda})=1.2\hspace{0.17em}\text{R.R.P.}(0),$$
(11)
$$kM>16:\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\text{L.R.P.}=10.88W(dD/dn)(dn/d\mathrm{\lambda})/kM,$$
(12)
$$0<kL<1:\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\text{L.R.P.}=1.2L(dn/d\mathrm{\lambda})$$
(13)
$$kL>16:\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\text{L.R.P.}=10.88(dn/d\mathrm{\lambda})/k.$$
(14)
$$2\hspace{0.17em}\text{cos}\hspace{0.17em}sfw+\left(s+\frac{1}{s}\right)\hspace{0.17em}fw\hspace{0.17em}\text{sin}\hspace{0.17em}sfw-2\hspace{0.17em}\text{cosh}\hspace{0.17em}fw=0.$$
(15)
$$\underset{fw\to 0}{\text{Lim}}\hspace{0.17em}sfw=2\pi .$$
(16)
$$6+({r}^{2}{f}^{2}{w}^{2}-6)\hspace{0.17em}\text{cos}\hspace{0.17em}rfw-4rfw\hspace{0.17em}\text{sin}\hspace{0.17em}rfw=0$$