Page 193 - A Practical Introduction to Optical Mineralogy
P. 193

ISOTROPY
                       Light of the same wavelength and the same or different intensity may
 4 Transmitted-light   be in  phase as  illustrated in  Figure 4.lb, or out of phase as  shown  in
                     Figure 4.lc. The path difference may be  measured as a fraction  of the
 crystallography     wavelength.
                       If two coherent rays (originating at the same instant from  the same
                     source)  which  are  exactly  in  phase  are  combined,  they  are  added
                     together and intensity is enhanced. If the rays are slightly out of phase,
                     the enhancement is  reduced. If the rays  have the same amplitude and
 4.1  Polarised light: an introduction
                      have a path difference of half a wavelength, the vibration will be cancel-
                      led and amplitude will  be zero.
 Light  is  an  electromagnetic  vibration  but,  for  the  purpose  of
                       In transmitted-light microscopy, linearly polarised white light travels
 transmitted- (and reflected) light microscopy, light can be considered as   up the microscope axis, which is normal to the plane of the thin s~ction.
 being simply the transfer of energy by vibrating 'particles' along a path
                      On  entering  an  anisotropic  (see  Section  4.3)  crystalline  substance
 from  the  source  to  the  observer.  White  light  consists  of many  rays,
                      rotated from  the extinction position, the light can  be considered to be
 ranging in wavelength from 380 to 770 nm through the visible spectrum.
                     separated  into  two  components which  travel  with  different velocities
 However, it is simpler to consider the idealised case of a single ray of
                      through the crystal. On leaving the crystal the two components may be
 monochromatic light, that is light of a single wavelength (Fig. 4.la). The
                     out of phase and the path difference will vary for different wavelengths
 wave is generated by vibration of particles (e.g. A) lying along the path
                     of light. This complexity in the light leaving the crystal is only apparent
 of the ray. If the light is non-polarised, the particles vibrate at random in
                      when  the  analyser  is  inserted and  interference colours  are generated
 a plane normal to the direction of the ray. If the light is linearly (or plane)
                      (see Section  4.6).
 polarised by means of a polarising filter, then the particles simply vibrate
 up and down  along the line  xy.
                     4.2  Refractive index
                      The refractive index of a medium (RI or n) is defined as the ratio of the
 ~~v  v               with wavelength but the variation is  usually small for transparent min-
                      velocity of light in  the medium to that in vacuo. Refractive index varies
                      erals, so  single ' white light'  refractive  indices are  usually used.
 A
                       If V,  and V 2  are the velocities of light in  two different media, and i is
 X
                      the angle  of incidence of the light  in  one medium and r is  its angle of
                      refraction  in  the other, then  (see Fig. 4.2):
                           ~     be    b'c sin i   sin i   refractive  index
 (b)                        v2   b'c'   b'c sin r   sin r
                      The refractive index of a  medium  is  inversely proportional to the vel-
                      ocity  of  light  (for  a  specific  wavelength)  through  the  medium,  i.e.
                      RIa:  1/V.
 (c)                 4.3  Isotropy

                     Isotropic crystals transmit light with  equal velocity in  all  directions. A
                     ray  velocity  surface  represents  the  surface  composed  of  all  points
 Figure 4.1  (a) Monochromatic light.  (b) Two waves  of the same wavelength,   reached by light  travelling along all  possible rays  from  a  point source
 but  different  intensity,  in  phase.  (c) Two  waves  of the  same  wavelength,  but   within  a  crystal  in  a  given  time.  In  isotropic crystals,  the ray  velocity
 different intensity, out of phase.   surface is  a sphere.
 180                 181
   188   189   190   191   192   193   194   195   196   197   198