2, Place a specimen crystal on the stage and center it at the intersection of the eyepiece ... This gives the retardatio
Instruction Manual
n1
OLWUS BEREK COMPD!SATOR
The Olympus Berek Compensator i s p r i m a r i l y intended for: a)
The a c c u r a t e measurement o f r e t a r d a t i o n i n double r e f r a c t i n g media.
b)
Determining t h e o p t i c a l c h a r a c t e r of t h e double r e f r a c t i o n .
This compensator can be i n s e r t e d i n t o t h e s l o t o f t h e i n t e r m e d i a t e p o l a r i z i n g tube f o r t h e Olympus Polarizing Microscope.
A c a l c i t e incorporated i n t h i s compensator L s designed t o be perpendicular t o
t h e o p t i c a l a x i s of t h e microscope a t t h e 30" d i v i s i o n l i n e f o r t h e i n s e r t i o n o r removal o f t h e compensator; otherwise t h e c a l c i t e edges might impinge a g a i n s t t h e s l o t of t h e i'nt'ermediate tube and be damaged.
I n s t r u c t i o n f o r Use
A.
I.
Align both t h e index l i n e s (one on t h e p o l a r i z e r o f t h e condenser and t h e o t h e r on t h e a n a l y z e r of t h e i n t e r m e d i a t e p o l a r i z i n g tube) a t t h e zero p o s i t i o n s ( t h i s is a c r o s s e d f i l t e r p o s i t i o n ) .
2,
Place a specimen c r y s t a l on t h e s t a g e and c e n t e r i t a t t h e i n t e r s e c t i o n o f t h e eyepiece c r o s s h a i r s .
-
3.
Rotate t h e s t a g e u n t i l t h e f i e l d i s dark.
This r e p r e s e n t s t h e p o s i t i o n
,-
of e v t i n c t i o n a s t h e o p t i c axis of t h e c r y s t a l i s p a r a l l e l t o t h e pl2ne of t h e p o l a r i z e r o r analyzer. A t t h i s p o s i t i o n , p u l l the-45" c l i c k s t o p l e v e r of t h e s t a g e toward t h e
o b s e r v e r a l l t h e way so t h a t t h e s t a g e can be c l i c k stopped a t diagonal position.
-
.
NOTE:
I)
This simple l e v e r o p e r a t i o n c l i c k s t h e s t a g e i n i n c r m e n t s of
45'
from any p o s i t i o n wherever t h e s t o p l e v e r i s pulled.
To
r e l e a s e t h e s t a g e , push back t h e l e v e r . 2)
I n case of t h e P o l a r i z i n g Microscope Model POS, however, g i v e t h e s t a g e 45" r o t a t i o n by reading t h e v e r n i e r , s i n c e i t has no 45" s t o p lever.
4.
I n s e r t t h e compensator i n t o t h e s l o t and r o t a t e the v e r n i e r s c a l e of t h e compensator from t h e 30" d i v i s i o n l i n e t o e i t h e r d i r e c t i o n .
If the
i n t e r f e r e n c e c o l o r decreases t h e c r y s t a l i s i n t h e s u b t r a c t i v e p o s i t i o n , so proceed with t h e Berek readings. I f the interference color increases t h e c r y s t a l i s i n t h e additive position.
Rotate t h e s t a g e 90" i n r e v e r s e t o t h e s u b t r a c t i v e p o s i t i o n
.
C
:
-.
B.
and t a k e Berek readings,
Berek Readings Get m.uimum e x t i n c t i o n on e i t h e r s i d e o f t h e 30" position.
Let ( a ) and
(b) represent t h e readings e i t h e r s i d e s of t h e 30" p o s i t i o n on t h e v e r n i e r scale.
Calculation of Retardation (R):
C.-
1.
Find t h e d i f f e r e n c e between t h e Berek readings ( a ) and (b).
2.
Divide by 2 t o f i n d (i)
-
. . . . . . . . . . (i)
a) = (
2
(b)
3.
I n T a b l e I f i n d l o g a r i t h m of ( i ) .
4.
To f i n d l o g R, add log ( i ) log R = l o g ( i )
+ log
+ log
C.
C
l o g C = o p t i c a l c o n s t a n t f o r Lndividual Berek Example:
5.
Let 3.907 = t h e o p t i c a l c o n s t a n t of B e r e k
I n T a b l e I1 f i n d t h e a n t i l o g o f l o g R. You must f i n d c o r r e c t decimal point.
To do t h i s , t a k e t h e d i f f e r e n c e
between t h e m a n t i s s a and t e n , augment by 1, t h i s g i v e s t h e number of decimal points.
E.uample:
Mantissa = 11, t h e r e f o r e 11
2, o r 2 decimal p o i n t s (.00). T h i s g i v e s t h e r e t a r d a t i o n =pressed Example:
Berek reading
in
( a ) = 35.7Q,
my. ( b ) = 24.5"
I n T a b l e I f i n d log f ( i ) . . l o g f ( i ) 5.6
= . . . . . . . . . . . . . . . . 7.980
compensator c o n s t a n t l o g C =
.........
ll i s t h e mantissa.
887 i s t h e index number.' The a n t i l o g o f t h e index 887 = 771 I n s e r t decimal (.00) = 77.1 o r l o g R = 77.1 R e t a r d a t i o n (R) =
lmr
77m
3.907 11.887
- 10 + 1 e q u a l
R e t a r d a t i o n may be c a l c u l a t e d w i t h a s l i d e r u l e . Take t h e a p p r o p r i a t e v a l u e of 10,000 f ( i ) and m u l t i p l y i t by t h e v a l u e
.
C
10,000 E-xample:
This g i v e s t h e R e t a r d a t i o n i n m
P-
( a ) = 35.7",
( b ) = 24.5"
Table I11 g i v e s 10,000 f ( i ) = 95.4 C
10,000
= 0.808
( o p t i c a l c e n t e r 550 m )
P
Hence, 95.4 x 0.808 = 77.1 R = 77.1
mfl
R e t a r d a t i o n may a l s o be expressed i n f r a c t i o n s of t h e wavelength used by t h e formula. 8
=
R
0 = B i r e f r i n g e n c e o r double r e f r a c t i o n
1
R
= Measured r e t a r d a t i o n
A
= Wavelength o f l i g h t used
m e n t h e t h i c k n e s s o f t h e c r y s t a l i s known t h e amount o f double r e f r a c t i o n o r b i r e f r i n g e n c e may b e determined fmm t h e formula. 8
=Ne-No=-
R d
N e = v e l o c i t y o f e ~ t r a o r d i n a r yl i g h t wave No = v e l o c i t y o f o r d i n a r y l i g h t wave R
= measured r e t a r d a t i o n
d
= section thickness
( a l s o e x p r e s s e d i n mu,) I
The compensator c o n s t a n t s a r e found i n t h e f o l l o w i n g manner. Using a monochromatic l i g h t , wavelength
, the
compensator i s t u r n e d from
z e r o o r 30° p o s i t i o n u n t i l t h e f i r s t d a r k l i n e c o i n c i d e s w i t h t h e i n t e r s e c t i n g
c r o s s h a i r o f t h e eyepiece from e i t h e r d i r e c t i o n .
Let t h e s e be ( a , ) and (bl ),
t h e a n g l e o r i e n t a t i o n (i, ) corresponding t o a r e t a r d a t i o n o f
From Table I f i n d log f ( i , ) and s u b t r a c t log Hence, log C = l o g
A -
A
A
w i l l be:
(wavelength used).
log f ( i )
Any nth p a i r of bands may be used f o r determining t h e v a l u e of l o g C.
I n t h i s case: (in) Hence, l o g C = l o g n
(an)
+ log
-
(5n)
2
A - log
f (in)
The v a l u e o f l o g C determined by e i t h e r formula w i l l b e i d e n t i c a l .
DETE&'.fINATION OF OPTICAL CHARACTER
The amount o f t h e compensator i s marked f o r 2'
(slow) and X' ( f a s t ) =es
determining t h e o p t i c a l c h a r a c t e r o f t h e d i r e c t i o n o f o s c i l l a t i o n .
for
Therefore,
by t u r n i n g t h e v e r n i e r s c a l e o f t h e compensator t h e i n t e r f e r e n c e c o l o r s used f o r t h e d i s t i n c t i o n of t h e i n c r e a s e o r d e c r e a s e a r e v a r i e d w i t h i n a 'range of
3 orders, f o r instance:
(a)
Orthoscopic d e t e r m i n a t i o n . With t h e c r y s t a l i n t h e d i a g o n a l ; 45" t o t h e plane o f t h e p o l a r i z e r o r
-
a n a l y z e r ; and p a r a l l e l t o t h e slow a x i s o f t h e compensator; w h i l e t u r n i n g t h e compensator drum o b s e r v e whether t h e i n t e r f e r e n c e c o l o r i s i n c r e a s i n g o r d e c r e a s i n g ; i f i n c r e a s i n g - it f o l l o w s , t h a t t h e d i r e c t i o n o f o s c i l l a t i o n i s p a r a l l e l t o t h a t o f t h e compensator ( a d d i t i v e c a s e ) ; i f d e c r e a s i n g t h e d i r e c t i o n o f o s c i l l a t i o n i s v e r t i c a l t o t h a t o f t h e compensator ( s u b t r a c t i v e case).
(b)
Conoscopic observation. The drum of t h e compensator i s turned t o recognize t h e o p t i c a l c h a r a c t e r by t h e d i r e c t i o n s of movement of t h e isochromates of t h e i n t e r f e r e n c e
figure. I f t h e isochromate f i g u r e moves toward t h e c e n t e r o f t h e i n t e r f e r e n c e f i g u r e t h e o s c i l l a t i o n i s p a r a l l e l t o t h a t o f t h e Berek; a d d i t i v e position. I f s u b t r a c t i v e p o s i t i o n t h e isochromates of t h e i n t e r f e r e n c e f i g u r e w i l l move outward away from t h e c e n t e r of t h e i n t e r f e r e n c e f i g u r e .
Then, t h e
o s c i l l a t i o n o f t h e lightwave i s v e r t i c a l t o t h a t of t h e Berek.
o p t i c a l Constants o i ' ~ o m ~ e n s a t oNO. r
A
C 656y
D
589mfl
d
F 486my
00
P 2.k
Day 1igh t O p t i c a l Center 5 5 b y
log C
J.J--3d
d>3??d 3,2+*?,3
3 , 3R 9
C 10000 r;),
pcr2
nl770
al?8?
6,,33~
TABLB
I
Logarithm f i
-0
-1
.2
.3
-4
-5
.6
.7
- 8
.9
m
-
4.484
5.086
5.438
5.688
5.882
6.040
4174
6.290
6.392
6.484
6.566
6.642
6.712
6.776
6.83d
6.892
6.945
6.994
7.041
7.086
7.128
7.169
7.207
7.244
7.280
7.314
7.346
7.378
7.408
7.438
7.466
7 - 9 4 7.521
7547
7.572
7.596
7.20
7 - 6 3 7.666
7.688 7.881
7.709
7.730
7750
7.809
7.828
7.898
7.915
7.932
7.995
7.864 8.025
8.054
8.068
8.082
7.980 8.122
7.846 8.010
8.039
7.770 7.790 7.948,7.964 8.095 8.109
8.135
8.148
8.161
8.173
8.185
8.198
8.210
8221
8.233
8.244
8.256
8.267
8.278
8.289
8.300
8.321
8.331
8.341
8.371
8.400
8.419
8.429
8.438
8.352 8.447
8.361
8.391
8.310 8.410
8.456
8.465
8.381 8.473
I 0
8.482
8.491
8.499
8.508
8.516
8.524
8.532
8.541
8.549
8.557
1 1
B-564
8.580
8.588
8.595
8.603
8.610
8.618
8.625
8.632
12
8,640
8572 8.647
8.654
8.661
8.668
8.675
8.682
8.689
8.702
13
8.709
8.722
8.728
8.735
8.741
8.748
8.754
14
8.773
8.715 8.779
8.695 8.760
8.785
8791
8.797
8.803
8.809
8.815
8.820
8.826
15
8.832
8.838
8.843
8.849
8.855
8.860
8.871
8.877
16
8.888
8.893
8.898
8.904
8.909
8.914
8.866 8.919
8.924
8929
8.882 8.935
17
8940
8.945
8.950
8.955
8.960
8.965
8.969
8.974
8.979
8.984
18
8.989
8.993
8.998
9.003
9.007
9.012
9.017
9.021
9.026
9.030
I9
9.035
9.039
9 , 0 4 4 9.348
9.053
9.057
9.062
9.066
9.070
9.075
20
9.079
9.083
9.087
3.092
9 . 0 9 6 ; 9.103
9104
9.108
9.112
9.116
-2 1
9.120
9.124
9.128
9.132
9.136
I 9.143
9.144
9.148
9.152
9.156
22 23
9.1 6 0 9.1 9 8
9.164
9.1 6 8
9.175
9.1 7 9
9.183
9.187
9.190
9.1 9 4
9.2 1 2
9.2 1 6
9.220
9.23
9.2 2 7
9.230
24
9.234 9.268
9.237
9.172 9.205 9.209 9.24 1 9.244
9.248
9:25 1
9.255
9.262
9.265
9.295
9.298
9.305
9.282 9.285 9.3.14 9.318
9.288
9.301
9.275 9.308
9.258 9.292
9.321
9.324
9.327
9.330
9.333 9.336 9.364 9.367
9.539 9.370
9.346
9.349
9.352
9.355
9.358
9.361
2379
9.387
9.390
9.396
9.399
9.382 9.410
9.384
9.393
9.3-73 9.376 9.402 9.405
9.413
9.416
9.419
9.421 9.448
9.424
9.427
9.430
9.443
9.451
9.454
9.456
9.438 9.441 9.464 9.467
1 2 3 4 5 6 7 8 9
25 26 27 2'8 29 30 31 r
(i)
9.20 1 9.272
I
9.278 9.51 1 9.343
9.407
9.43.2 z 4 3 5 9.459 9.462
8.766
9.446 9.469. 9.472
TABLE
11
Logarithm Of T h e Natural Number8
N
0
I
2
3
4
5
6
7
8
9
10
000
004
009
013
017
021
025
029
033
037
1 1
041
045
049
053
057
061
064
068
072
076
12
079
083
086
090
093
097
100
104
107
1 1 I
13
114
117
121
124
127
130
I34
137
140
143
14
!46
152
155
158
161
164
167
170
173
15
176
149 179
181
185
188
190
193
196
199
16
204
207
210
212
215
217
220
223
225
201 228
17
230
233
236
238
241
243
246
248
250
253
18
255
258
260
262
265
267
270
272
274
276
19
279
281
283
286
288
290
292
294
297
299
20
301
303
305
307
310
312
314
3
318
320
2 1
322
324
326
328
330
332
334
336
338
340
22
342
344
346
348
350
352
354
356
358
360
23
362
364
365
367
369
371
373
375
377
378
24
380
382
384
386
387
389
391
393
394
396
25
400
401
403
405
407
408
410
412
413
26
398 415
417
418
420
422
423
425
427
430
27
431
433
435
436
438
439
441
442
428 444
28
447
449
450
452
453
455
456
458
459 474
461 476
446
29
462
46.4
465
467
468
470
471
473
30
477
479
480
481
483
484
486
489
-31
491
493
494
496
497
498
500
487 501
502
490 504
516
517
32
505
507
508
509
511
512
513
515
33
519
520
521
522
524
525
526
528
529
3 4
533
534
535
537
'538
539
540
542
35
53j 564
530 543
545
547
548
549
550
551
553
554
555
36
556
558
559
560
561
562
563
565
566
567
3 7
568
569
571
572
573
574
575
576
577
579
38
580
581
582
503
584
585
587
588
589
39
591
592
593
594
595
597
598
599
600
590 601
40
602
604
605
60.6 - 6 0 7
609
610
61 1
612
4 1
613
603 614
615
616
617
619
620
621
622
618
, TABLE
11
(Continued)
N
0
1
2
3
4
5
6
7
8
9
42
623
624
625
626
627
628
629
630
632
43 44
633
634
635
636
637
638
639
640
631 641
643
644
645
646
647
648
649
650
651
652
45
653
654
655
656
657
659
662
663
664
665
673
677
678
679
681
682
674 683
670 679
671
672
667 676
668
47 48
666 675
660 669
661
46
658 667
684
685
687
689
49
690
691
692
693
694
686 695
695
696
688 697
50
700
701 708. 709
702 710
702
703
704
705
706
707
5 1
699 708
712
713
713
714
52
716
717
718
718
711 719
720
721
722
715 723
53
724
725
726
727
728
728
729
730
723 731
733
734
735
736
736
737
739
739
760
742
743
744
744
745
766
747
767
751
752
753
754
754
755
54 55
732 740
741
642
680 689 698
732
56
748
749
750
751
57
756
757
757
758
759
760
760
761
762
763
58
763
764
769
769
770
772
774
767 775
768
771
766 773
766
59
765 772
775
776
777
777
60
778
779
780
780
781
782
783
784
785
61
785
786
787
787
788
790
791
792
62 63
792
793
794
794
795
789 796
782 790 797
797
799
799
800
801
801
802
803
803
804
798 805
805
64
806
807
808
808
809
810
811
812
812
65
813
814
814
815
816
816
810 817
818
818
819
66 67
920 87-6
820
822
822
.,823
823
824
825
825
827
821 827
828
829
829
830
831
831
832
68 69
833
833
834
834
836
836
837
839
840
841
842
843
843
838 844
838
839
835 841
70
845
846
846
847
848
848
849
850
7 1
851
852
854
854
856
857 863
853 859 865
861
862 867
856 862
851 857
72 73
852 858 864
849 855
859 865
-
860 860 866-866
867
868
864
863 869
TABLE I1 (Continued)
N
0
1
2
3
4
5
6
7
8
9
74
8 6 9
870
870
8 7 1
8 7 2
8 7 2
873
873
8 7 4
8 7 4
75
875
876
876
8 7 7
8 7 7
8 7 8
8 7 9
8 7 9
880
880
76
8 8 1
881
8 8 2
883
8 8 3
884
884
885
885
886
77
886
887
8 8 8
8 8 8
8 8 9
8 8 9
890
890
891
8 9 2
78
892
893
893
8 9 4
8 9 4
895
895
896
897
897
79
8 9 8
898
8 9 9
8 9 9
900
900
901
901
902
903
80
903
904
904
905
905
906
906
907
907
908
8 1
908
909
910
910
911
911
912
912
913
913
914
914
915
915
916
916
917
918
918
9 1 9
921
922
922
8 2 3
923
924
8 2 8 3
919
920
920
9 2 1
8 4
924
925
925
926
926
927
927
928
928
929
85
9 2 9
930
9 3 0 ;
931
931
932
9.32
933
933
934
8 6
934
935
936
936
937
937
938
938
939
9 3 9
8 7
94n
940
941
941
942
942
942
943
943
944
88
944
945
945
946
946
947
947
948
948
949
8 9
9 4 9
950
950
951
951
952
952
953
953
954
90
954
955
955
955
956
957
957
958
958
959
9 1
959
960
960
960
961
961
96'2
962
963
963
9 2
964
964
965
965
966
966
967
967
968
968
93
968
969
969
970
970
971
971
972
972
973
94
973
974
974
975
975
975
976
976
977
977
95
978
978
979
9 7 9
980
980
980
981
981
982
96
982
983
983
984
984
985
985
985
986
986
9 7
987
987
988
988
989
9 8 9
989
990
990
991
98
991
992
992
9 9 3
9 9 3 - 9 9 3
994
994
995
995
99
996
996
997
997
997
998
9 9 9
999
000
998
TABLE
111
r o o o f (i) i
.O
1
.2
.3
,
d
.5
.6
.7
0
0.0
0.0
0. 1
0.3
a5
0.8
I. 1
1.5
1
3.0
3.7
5. 1
6.0
6.9
7.8
8.8
2
12.2
13.4
4.4 14-71
17.5
19.0
20.6
22.2
3 4
27.4 48.4
29.3
31.2
16.1 33.2
37.3
39.5
53.7
56.3
5
76.1
51.2 79.1
35.2 58.9
823
85.5
88.7
61.6 92.0
6
109.5
116.9
120.7
124.6
128.5
7
149.0
113.2 153.3
157.6
162.0
166.5
8
194.5
199.3
204.3
209.3
9
257.4
257.0
262.6
10
245.9 3a54
309.5
1 1
346.8
373.5
12
436.1
443.4
13
511
519
5?7
14
592
601
15
679
16
772
688 781
17
870
18 19
974
880 985
1084
20
.8
1. 9 9.9
.9 25 1l.g 25.6
41.7
259 44.0
46.3
64.4
67.2
70.1
73.1
98.6 136.5 180.2
102.3 140.6 184.9
105.9
171.0
95.4 132.5 175.6
214.4
219.5
224.6
229.9
235.2
240.5
268.2
273.9
279.7
285.5
291.4
3 1 5 . 6 321.8 328.1 380.2 -387.0 393.8 450.7 4 5 8 - 1 4 6 5 . 5
334.4
340.7
347.2
3457
297.4 36az
400.8
407.7
421.8
428.9
473.0
480.6
414.7 488.2
495.8
503.5
535
543
551
559
567
576
584
609 697
618
626
635
644
653
661
670
706
716
725
734
743
753
762
791
801 901
810
820
830
840
860
91 1
932
1006
1017
942 1050
1095
996 1306
921 1028
850 953
1118
1129
1141
1199
1211
1222
1234
1246
1258
2 1 - 22
1319
1332
1344
1357
1369
1382
1445
1458
1471
1484
1497
1523
23
1577
1590
1617
1631
1658
24
1713
1727
1603 1741
1510 1644
1407 1537
1755
25
1869
1884
1898
26
1855 2001
1769 I783 1913"1927 2062
2153
2032 2184
2046
27
2016 2169
2200
28
2310
29
2471
2326 2488
2342 2504
30
2637
2654
3 1
2808
2825
890
144.8 189.6
1061
963 1072
1175
1187
1295 1420
1307 1432
1550
1563
1672
1685
1699
1797
1812
1826
1840
1957
1972
1987
2077
1942 2092
2107
2123
2138
2215 2374
2231 2390
2247 2407
2262
2278
2294
2439
2455
2554
2570
2722
2739
2756
2604 2773
2620
2671
2-521 2 5 3 7 2688 2705
2422 2587
2843
2860
2877
2895
2912
2930
2947
2965
2358
1039 1152 1270 1394
1164 1283
2791
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