## Abstract

With this eyepiece the plane-polarization in a beam of light is compensated by means of a thin, plane-parallel plate of celluloid tilted at the proper angle. To ascertain if the compensation is complete a detector consisting of a quartz plate and a second tiltable plate of celluloid is used in combination with a Savart plate and a nicol or Wollaston prism. The biquartz plate consists of two plates of quartz cut normal to the optic axis, the one of dextrogyre and the second of laevogyre quartz, mounted side by side with polished junction faces. The thickness of the quartz plates is such (1.76 mm) that for mercury green light of wave-length 5461A the rotation is ±45°. An incident plane-polarized beam is divided into two beams by the biquartz plate; the plane of vibration of the beam emerging from the first half of the plate is normal to that of the second beam. The tiltable plate of the detector is mounted above the biquartz plate and has its axis of rotation in the plane of vibration of the wave emerging from one of the biquartz plate halves. By means of this second plate a small amount of polarization can be added to, or subtracted from the polarization in the transmitted beams. The Savart plate and analyzing prism serve to detect the presence of plane-polarized light in the beam. With the aid of this eyepiece the amount of plane-polarization can be determined, for low percentages, to one-fifth of one percent. The eyepiece has been used chiefly in the measurement of the percentage plane-polarization in light reflected by different parts of the moon’s surface and by terrestrial materials; also for the measurement of sky polarization and in metallographic work.

© 1934 Optical Society of America

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### Equations (22)

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(1)
$$\begin{array}{l}Rp={\text{tan}}^{2}\hspace{0.17em}(i-r)/{\text{tan}}^{2}\hspace{0.17em}(i+r)\\ Rn={\text{sin}}^{2}\hspace{0.17em}(i-r)/{\text{sin}}^{2}\hspace{0.17em}(i+r).\end{array}$$
(2)
$$Tn={(1-Rn)}^{2}(1+R{n}^{2}+R{n}^{4}+\cdots )={(1-Rn)}^{2}/(1-R{n}^{2})=(1-Rn)/(1+Rn),$$
(3)
$$Tp=(1-Rp)/(1+Rp).$$
(4)
$$P=(Tp-Tn)/(Tp+Tn).$$
(5)
$$\text{tan}\hspace{0.17em}An=\text{sin}\hspace{0.17em}(i-r)/\text{sin}\hspace{0.17em}(i+r)$$
(6)
$$\begin{array}{c}\text{tan}\hspace{0.17em}(45\xb0-An)=\text{tan}\hspace{0.17em}r/\text{tan}\hspace{0.17em}i,\\ \text{tan}\hspace{0.17em}Ap=\text{tan}\hspace{0.17em}(i-r)/\text{tan}\hspace{0.17em}(i+r)\end{array}$$
(7)
$$\text{tan}\hspace{0.17em}(45\xb0-Ap)=\text{sin}\hspace{0.17em}2r/\text{sin}\hspace{0.17em}2i,$$
(8)
$$Tn={\left(\frac{1-Rn}{1+Rp}\right)}^{2}\times \left(1+\frac{R{n}^{2}(1-Rn)}{(1-Rn)[1-R{n}^{2}{(1-Rn)}^{2}]}\right)$$
(9)
$${C}_{0}\hspace{0.17em}{\text{tan}}^{2}\hspace{0.17em}r+2{C}_{1}\hspace{0.17em}\text{tan}\hspace{0.17em}r+{C}_{2}=0,$$
(10)
$${C}_{0}={\text{sin}}^{2}\hspace{0.17em}i\xb7[{e}^{2}+({o}^{2}-{e}^{2})\xb7{\text{sin}}^{2}\hspace{0.17em}\vartheta \xb7{\text{cos}}^{2}\hspace{0.17em}\zeta ]-1,$$
(11)
$${C}_{1}={\text{sin}}^{2}\hspace{0.17em}i\xb7({o}^{2}-{e}^{2})\hspace{0.17em}\text{sin}\vartheta \xb7\text{cos}\hspace{0.17em}\vartheta \xb7\text{cos}\hspace{0.17em}\zeta ,$$
(12)
$${C}_{2}={\text{sin}}^{2}\hspace{0.17em}i\xb7({o}^{2}\hspace{0.17em}{\text{cos}}^{2}\hspace{0.17em}\vartheta +{e}^{2}\hspace{0.17em}{\text{sin}}^{2}\hspace{0.17em}\vartheta ).$$
(13)
$$\text{tan}\hspace{0.17em}{r}_{\u220a1}=(1/{C}_{0})[-{C}_{1}\pm ({{C}_{1}}^{2}-{C}_{0}{C}_{2}{)}^{{\scriptstyle \frac{1}{2}}}],$$
(14)
$$\text{tan}\hspace{0.17em}{r}_{\u220a2}=(1/{C}_{0})[+{C}_{1}\pm ({{C}_{1}}^{2}-{C}_{0}{C}_{2}{)}^{{\scriptstyle \frac{1}{2}}}].$$
(15)
$${\mathrm{\Delta}}_{1}=((d\xb7\text{sin}\hspace{0.17em}i)/\mathrm{\lambda})(\text{cot}\hspace{0.17em}{r}_{\u220a1}-\text{cot}\hspace{0.17em}{r}_{\omega}),$$
(16)
$${\mathrm{\Delta}}_{2}=((d\xb7\text{sin}\hspace{0.17em}i)/\mathrm{\lambda})(\text{cot}\hspace{0.17em}{r}_{\u220a2}-\text{cot}\hspace{0.17em}{r}_{\omega}),$$
(17)
$${\mathrm{\Delta}}_{1}-{\mathrm{\Delta}}_{2}=((d\xb7\text{sin}\hspace{0.17em}i)/\mathrm{\lambda})(\text{cot}\hspace{0.17em}{r}_{\u220a1}-\text{cot}\hspace{0.17em}{r}_{\u220a2}).$$
(18)
$$\begin{array}{l}{\mathrm{\Delta}}_{1}-{\mathrm{\Delta}}_{2}=\frac{2\xb7d\hspace{0.17em}\text{sin}\hspace{0.17em}i}{\mathrm{\lambda}}\xb7\frac{{C}_{1}}{{C}_{2}}\\ =\frac{d\xb7\text{sin}\hspace{0.17em}i}{\mathrm{\lambda}}\xb7\frac{2\xb7\text{sin}\hspace{0.17em}2\vartheta \xb7\text{cos}\hspace{0.17em}\zeta}{({o}^{2}+{e}^{2})/({o}^{2}-{e}^{2})-\text{cos}\hspace{0.17em}2\vartheta}.\end{array}$$
(19)
$${\mathrm{\Delta}}_{1}-{\mathrm{\Delta}}_{2}=0.15453104\xb7((d\xb7\text{sin}\hspace{0.17em}i)/\mathrm{\lambda})=262.21924\xb7d\xb7\text{sin}\hspace{0.17em}i.$$
(20)
$$d\xb7\text{sin}\hspace{0.17em}i=\mathrm{0.0038136.}$$
(21)
$$I={\text{cos}}^{2}\hspace{0.17em}\phi ,$$
(22)
$$P=({T}_{1}-{T}_{2})/({T}_{1}+{T}_{2})=(1-{\text{cos}}^{2}\hspace{0.17em}\alpha )/(1+{\text{cos}}^{2}\hspace{0.17em}\alpha )=\text{cos}\hspace{0.17em}2\beta $$