22 BELL SYSTEM TECHNICAL JOURNAL 



ordinary reflection laws, and the whole groups of facets act similarly to a 

 single mirror surface at the same angle, as in B.^ The individual facets 

 being very minute and of irregular size and spacing, however, cause appre- 

 ciable diffusion of the beam. The resultant effect of all three sets of facets 

 is shown in C, where light passing down through a lens and a hole in the 

 screen is reflected back to three spots on the screen. These three spots are 

 located at equal distances from the incident beam and at 120° intervals 

 around the incident beam. If the quartz section be rotated on its table the 

 spots rotate around the screen correspondingly. However, lateral motion 

 of the section across the table (without rotation) does not change the 

 position of the spots, if the section be untwinned. If the section is twinned 

 (or more exactly, if the etched surface is twinned) the three-fold figure will 

 shift to a different position (angularly) on crossing a twinning boundary, 

 for the etch pits are oriented differently in the two twins. If the twinning 

 boundary divides the illuminating beam, then both figures appear at once, 

 giving six spots instead of three. It is clear then that twinning, as well as 

 orientation of the section, may be determined from the figure on the screen. 

 The angular relation between the spots and the X-axes of the section will 

 be considered later, where figures of actual sections are shown. 



The long used method of examining etched quartz surfaces by simple 

 reflection from a bright light, may also be explained from Fig. 5.7C. If a 

 spot of light on the screen is viewed along the line E, and the screen then 

 removed, the light from the associted etch-pits will fall on to the eye. The 

 illuminated portion of the section will appear bright. If a twinning bound- 

 ary crosses the illuminating beam and one of the sbc reflected beams falls 

 on the eye, one of the two illuminated twins will appear bright and the 

 other dark. As the section is rotated, first one twin and then the other will 

 appear bright, and in each case the twinning boundary is sharply defined 

 over the whole region covered by the illuminating beam (the appearance of 

 twinned Z-cut surfaces examined by this means is shown in Figs. 5.1, 5.2, 

 5.3). Due to the greater complexity of etch-pits than here idealized, the 

 reflected beams are not so sharply defined as to require exact location of the 

 eye relative to the incident beam and the section. Further, when a broad 

 unfocused light source is used, it is possible and convenient to detect twin- 

 ning boundaries merely by holding the section in the hand and rocking it 

 about in various directions until a brightness contrast is observed. Though 

 the brightness contrast is usually not marked by this simple examination it 

 suffices for many purposes. 



^ That the effect of a group of facets is not identically the same as that of a single mirror, 

 is of more concern where lenses are used for focusing. In this case the displacement of the 

 mirror facets causes a displacement of the focus of the beam from each facet. For beams 

 of small angular range this is of little importance. 



