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666

Projector fo r interference f igures an d fo r directm e a s u r e m e n t o f 2 VB y H . C . G . VINCENT M . A . , A . R . I . C . , F . G . S .

D e p a r t m e n t o f G e o l og y , U n i v e r s i t y o f C a p e T o w n .[Taken as read M arch 24, 1955.]

H E i n s t r u m e n t is d e s ig n e d f o r t h e s t u d y a n d m e a s u r e m e n t o f t h eo p t i c a l c h a r a c t e r s o f c r y s t a l s a n d a n i s o t r o p i c m a t e r i a ls . T h e c o n o -

s c o p ic p h e n o m e n a , o v e r a w i d e a r e a f o r a n y s e l e ct e d o r i e n t a t i o n o f t h es p e c i m e n , m a y b e b r o u g h t i n t o v i e w o n a h e m i s p h e r i c a l s c r e e n , w i t h o u tt h e u s e o f a m i c r o s c o p e o r l en s s y s te m . T h e p a r t s o f t h e i n t e r f e r e n c ef ig u r e r e t a i n t h e i r t r u e a n g u l a r r e l a t io n s h i p s, d i r e c t l y d i s p l a y i n g f o ro b s e r v a t i o n o r m e a s u r e m e n t v a l ue s o f 2 V f o r a n y a n g u l a r s e p a r a t i o n o ft h e o p t i c a x e s .

T h e p o l a r iz i n g m i c r o s c o p e h a s c e r t a i n l i m i t a t i o n s ; f o r e x a m p l e , o b s e r -v a t io n s , u s u a l l y m o n o c u l a r , c a n b e m a d e o n l y b y o n e p e r s o n a t a t i m ea n d e r r o rs o f i n t e r p r e t a t i o n m a y a r is e . T h e f i x ed p o s i t io n o f t h e c r y s t a li n i ts m o u n t a l lo w s n o c h a n g e o r ch o i c e o f o r i e n t a ti o n . I n a d d i t i o n , t h es i g n if i ca n t a r e a o f t h e f ig u r e is r e s t ri c t e d , n o t o n l y b y t h e l e n s s y s te m ,b u t a l s o b e c a u s e t h e a p p a r e n t a n g l e in ai r, 2 E a n d n o t 2 V , is o b s e r v e d ,s o t h a t o n l y a m i n o r p o r t i o n o f t h e c o n v e r g e n t p h e n o m e n a is vi si bl e int h e f ie ld o f v i e w o f t h e m i c r o s c o p e , a n d o n l y s m a l l o p t i c a x i a l a n g l es e p a r a t i o n s m a y b e o b s e rv e d . T h e m i c r o s c o p e p r o j e c t o r h a s t h e s i n gl ea d v a n t a g e t h a t t h e f i gu re m a y b e v i e w e d o n a fl a t s c re e n b y a g r o u p o fo b s e r v e r s u s i n g n o r m a l v i si o n . H o w e v e r , th i s e q u i p m e n t is e l a b o r a t ea n d u n s u i t a b l e f o r i n d i v i d u a l s tu d i e s a n d m e a s u r e m e n t s . T h e o p t i c a x i a lg o n i o m e t e r a n d t h e u n i v e r s a l s t a g e a re a v a il a b l e f o r q u a n t i t a t i v e w o r k ,b u t s p e c i a l t e c h n i q u e s r e s t r i c t t h e i r u s e . T . T . Q u i r k e 1 h a s d e s c r i b e dm e t h o d s f o r p r o je c t i o n a n d m e a s u r e m e n t , u s in g a c o n v e r g i n g le n ss y s t e m a n d c r y s t a l se c t io n s w i t h f ix e d o r i e n t a t io n . T h e p r o c e d u r e i sb a s e d o n t h e a p p a r e n t a x i a l a n g l e 2 E ) , g iv i n g a l i m i t e d e f f e c t i v e f ie ld ,a n d i s t h e r e f o r e a p p l i c a b le t o c r y s t a l s w i t h s m a l l a x i a l a n g le s . H . W i n -

1 T. T. Quirke, Direct projection of optic figures. Am er. Min., 1938, vol. 23,pp. 595-605. [M.A. 7 249.]

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P R O J E T O R F O R I N T E R F E R E N E F I G U R E S 6 6 7c h e l l d e s c r i b e s t h e u s e o f c u t s p h e r e s m a d e o f c r y s t a I s s u c h a s c o r u n d u mo r q u a r t z , f o r d e m o n s t r a t i o n o f o p t i c f ig u re s w h e n m a n i p u l a t e d b e t w e e np o l a r o i d sh e e ts . T h e i n t e r f e r e n c e f ig u r e m a y b e v i e w e d in s i d e t h e s p h e r ea n d p r o j e c t i o n c a n b e a r r a n g e d . Q u i t e r e c e n t l y , C . S . H u r l b u t , b y p l a c i n ga g l a s s ( or p l a s t ic ) s p h e r e a b o v e t h e c r y s t a l se c t io n , s h o w s t h e i n t e r -f e r e n c e f i g u r e r e f l e c t e d i n a m i r r o r . ~

I n t h e m e t h o d h e r e d e s c ri b e d , t h e c r y s t a l , m o u n t e d a t t h e c e n t r e o f at r a n s p a r e n t s p h e r e , i s c a p a b l e o f f r e e r e v o l u t i o n a b o u t i t s c e n t r e , a n d i si l l u m i n a t e d b y p o l a r i z e d l i g h t c o n v er g i n g u p o n i t a t a w i d e a n g l e fr o ma r e fl e ct o r. T h e e m e r g e n t r a y s tr a v e r s e t h e a n a l y s e r , a n d c o m b i n e top r o d u c e a f o c u s e d i m a g e o f t h e i n t e r f e r e n c e f i g ur e o n th e s p h e r i c a l s u r-f a c e o f t h e s c r ee n . T h e c u r v a t u r e a n d : p o s i t i o n o f t h e s c r e e n a r e soa r r a n g e d t h a t t h e s p h e r e . a n d s c r e e n : a r e c o n c e n t r ic w h e n t h e i n t e r -f e r e n c e f ig u r e i s i n f o cu s o v e r V he w h o l e o f t h e s c r ee n . T h e p h e n o m e n am a y b e e x a m i n e d w h i l e t h e s p h e r e is r e v o l v e d , g i v i n g i n e ff e c t a w o r k i n gm o d e l o f t h e c r y s t a l a n d i t s i n d i e a t r i x fo r a n y d e s i re d o r i e n t a t i o n . T w oo p t i c a x e s m a y b e s e en a t o n e t i m e o n th e s c re e n , f o r a n a n g u l a r s e p a r a -t i o n o f u p t o 1 2 0 d e g r e e s , s o t h a t t h e t r u e o p t i c a x i a l a n g l e , 2V a c u t e ,o f a n y m a g n i t u d e m a y b e d i r e c t ly m e a s u r e d u p o n t h e s cr e en . S i m p l ei n u se a n d c o n s t r u c ti o n , t h e i n s t r u m e n t is s u i t a b le f o r b o t h c l a ss d e m o n -s t r a t i o n a n d i n d i v i d u a l o p e r a t i o n ; a n d , w h e n t h e d i m e n s i o n s o f t h es c re e n a n d i ts p o s i t i o n i n g a r e c o r r e c t ly a r r a n g e d , a c c u r a t e a n d r e l ia b l ev a l u e s f or o p t ic a n g l e s a r e d i r e c t l y m e a s u r a b l e f o r c r y s t a l g r a in s o rp l a t e s o f a d i a m e t e r o f t w o m m . a n d u p w a r d s . B y r e m o v a l o f t h es c r e en , a n d a l so t h e s p h e r e w h e n n e c e s s a r y , a n d r e d u c t i o n o f t h e l i g h ta p e r t u r e , t h e i n s t r u m e n t is c o n v e r t e d t o a p a r a l l e l l i g h t p o l a r is c o p e .

T h e a p p a r a t u s i s s h ow n , a s a p a r t i a l l y d i a g r a m m a t i c s e c t io n a l v i e w ,i n f ig . 1. T h e o v e r a l l d i m e n s i o n s t h e r e i l l u s t r a t e d a r e a d e q u a t e f o r m u c hl a r g e r s p h e r e a n d s c r e e n . T h e s p h e r e , A , i s c o n s t r u c t e d o f t w o e q u a ls e g m e n t s o f g la s s. ~ E a c h s e g m e n t h a s , c e m e n t e d t o i t s p l a n e s u r f a c e , am e t a l r in g , t h e r i n g on o n e s e g m e n t b e i n g a n a c c u r a t e f i t w i t h i n t h a t o nt h e o t h e r , a n d t h e d i m e n s i o n s a r e s uc h t h a t , w h e n a s s e m b l e d , t h e s eg -m e n t s a r e s e p a r a t e d b y a n a r r o w s p a c e to a c c o m m o d a t e t h e c r y s ta l , a n de x t e r n a l l y f o r m a s p he r e , w i t h t h e o u t e r m e t a l r i n g f o r m i n g p a r t o f t h es u r f a c e .

1 H. W inchell , De m on stratio n of interference figures. Am er. Min., 1947, vol. 32,pp . 588-589. [M .A . 10 468.]2 C. S. Hu rlb ut, J r. , D em ons tratio n polariseope. Am er. Min., 1955, vol. 40.pp . 120 122.3 H . C. G. Vincent, M in. M ag., 1954, vol. 30, p. 513.

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668 H . c . G . V I N C E N T O NThe sphere is supported in the central opening of the circular metal

stage B which rota tes in a recess in the cover C of the reflector. Theopening has three equally spaced hardened steel balls D let into its

~ \ I I _ _

c B

I-

, / I ~ ' ' '~ . . /\ ,,, /: 2

r : l ~ f . l A1 I0 I ' ~ L

FIG. l. Projection apparatus in convergent light. A sphere B stage C coverD ball supports E reflector F lamp G switch H plug I water cell J polarizerK inner ring L analyser M viewing screen N outer ring 0 groove P horizontal armQ post R adjustable stop S masking tube T strip.circumference and adjustable in position. The sphere re volves freely onthis three-poin t Support and the small clearance between the sphere an dthe plate may be screened by a ring of black velvet.

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P R O J E C T O R F O R I N T E R F E R E N C E F I G U R E S 9

T h e c o v e r c a r r y i n g t h e s t a g e a n d s p h e r e f i t s o v e r t h e c i r c u l a r e d g e o ft h e r e f l e c t o r E . T h e s h a p e o f t h e r e f l e c t o r i s n o t c r i t i c a l b u t s h o u l d b ec h o s e n t o g i v e a s t r o n g c o n c e n t r a t i o n o f l i g h t o n t h e s p h e r e o v e r a w i d ea n g l e , a n d t h e l ig h t b u lb , F , s h o u l d b e a d j u s t a b l e i n h e i g h t . I l l u m i n a -t io n is c o n v e n i e n t l y p r o v i d e d b y s t a n d a r d l a m p s o n t h e m a i n s s u p p l y .T h e r e f l e c to r c a r r i e s t h e w a g e r c el l, I , t h e s u r f a c e o f w h i c h i s p r e f e r a b l yo f ' p e r s p e x ' o r s i m i l a r p l a s t i c , s a n d e d t o d i f f u s e t h e l i g h t f r o m b e l o w .T h e ce ll, f e d s l o w l y f r o m a c o n v e n i e n t s u p p l y , e f f e c ti v e ly a b s o r b s t h eh e a t a n d a l l o w s c o n t i n u o u s o p e r a t i o n e v e n w h e n h i g h e o n s m n p t i o nl a m p s a r e i n u se .

A c i r c u la r s h e e t o f p o l a r o id , t h e p o l a ri z e r, J , r e s ts u p o n t h e u p p e rs u r fa c e o f t h e c ell a n d i s o f a d e q u a t e d i a m e t e r t o a ll ow t h e m a x i m u ma n g l e f o r t h e c o n e o f r a y s e n t e r i n g t h e s p h er e .

T h e p r o j e c t i o n s c r e e n a n d u p p e r p o l a r o i d a s s e m b l y i s s u p p o r t e da x i a l l y a b o v e t h e s p h e re , a n d c o n s i s ts o f a n i n n e r m e t a l r in g , K , c a r r y i n gt h e p o l a r o i d a n a l y s e r , L , a n d t h e s c re e n ; M , w h i c h i s f r e e t o r o t a t e i n a no u t e r r in g , N . T h e s cr e en m a y b e m a d e f r o m a n a c c u r a t e l y b l o w ns p h e ri c al g r o u n d - g l a s s b u l b o f t h e p r o p e r d i a m e t e r . I t s r a d i u s o f c u r v a -t u r e s h o u l d b e e q u a l t o th e d i s t a n c e f r o m t h e c e n t r e o f t h e s p h e r e to t h ef o c a l p o s i t io n o f t h e i n t e r fe r e n c e f i gu re . T h e p o s i t i o n m a y b e f o u n d b yt r ia l , u s i n g th e o p t i c a x i a l fi g u re o f a t h i c k f la k e o f m u s c o v i t e m o u n t e di n t h e s p h e re , f o c u s e d o n t h e u p p e r s u r f a c e o f a s h e e t o f g r o u n d - g l a s sh e l d a b o v e . T h e i n n e r r in g , K , h a s a s h a l l o w c ir c u l a r g r o o v e , O , i n w h i c ht h e s c r e e n f its . R i n g a n d s c r e e n m a y e a c h b e i n d e p e n d e n t l y r o t a t e d .T h e d i sk o f p o l a r o id , L , i s f i t te d i n t o t h e c e n t r a l o p e n i n g , w h i c h is m a i n -t a i n e d a s l a r g e a s t h e s c r e e n w i ll a l lo w . T h e s c r e e n a s s e m b l y i s s u p p o r t e db y a s t o u t h o r i z o n t a l a r m , P , a d j u s t a b l e i n l e n g t h , w h i c h s l i d e s u p a n dd o w n a l o n g t h e r i g id v e r t ic a l p o s t , Q , f ir m l y a t t a c h e d t o t h e b a s e o f t h ei n s t r u m e n t . A n a d j u s t a b l e s t o p , 1 o n t h e p o s t f ix e s t h e c o r r e c t h e i g h ta n d p o s i t io n f o r t h e s c re e n , a t w h i c h p o i n t i ts s u r f a c e is t r u l y c o n c e n t r i cw i t h t h a t o f t h e s p he re , a n d t h e s c re e n a s s e m b l y m a y a l so b e s w u n g t oone s ide .

T h e r e l a t iv e p o s i ti o n s i n d i c a t e d a r e d e s i g n e d t o g iv e t h e m a x i m u me f f e c t i v e a r e a f o r t h e p r o j e c t i o n s c r e e n , a l l o w i n g i t t o d i s p l a y , f o r o n eg i v e n o r i e n t a t i o n o f t h e c r y s t a l , b o t h o p t i c a x e s w i t h a n a n g u l a r s e p a r a -t i o n o f u p t o a b o u t 1 2 0 d e g re e s, w i t h a s s o c i a t e d i n d i c a t r i x p h e n o m e n a ,o v e r a n a r e a o f a b o u t t w o - t h i r d s o f a h e m i s p h e r e .

T h e m a s k i n g t u b e , S , m a y b e s w u n g i n t o p o s i t io n t o l im i t t h e i n t e r -f e r e n c e f i g u r e v i s i b l e t o a s m a l l a r e a c o m p a r a b l e t o t h a t s e e n i n ap o l a r i z i n g m i c r o s c o p e , a n d i s u s e f u l i n t e a c h i n g .

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6 7 0 H c G VINCEN T ONA p e r s p e x o r g l as s s t ri p , T , o p e r a t e s t h r o u g h h o r i z o n t a l sl o ts o n

o p p o s i t e s id e s o f t h e r e fl e c to r a n d is a d j u s t a b l e i n h e i g h t s o t h a t t h es p h e re r e st s u p o n i t a n d t h e w e i g h t o f t h e s p h e r e is p a r t ia l l y t a k e n b yt h e s t r ip . T h u s , b y m o v i n g t h e s t r ip i n a n y d e s ir e d d i re c t i o n i n i ts h o ri -z o n t a l p la n e , t h e s p h e r e m a y b e r e v o l v e d o n a n y a x i s i n o rd e r to v a r yt h e o r i e n t a t i o n o f t h e c r y s t a l w h il e t h e s c r e e n is u n d e r o b s e r v a t i o n . T h ei n s t r u m e n t s h o u l d b e w e ll v e n t i l a te d a n d n e c e s s a r y p a r t s r e n d e r e d d u l lb l a c k o r s c re e n ed . I f t h e i n s t r u m e n t is n o t i n t e n d e d f o r a c c u r a t em e a s u r e m e n t , s p h e re a n d sc r ee n m a y b e m a d e o f p e r s p e x o r s im i la rp l as t i c .

P r o j e c t i o n i s b e s t w h e n t h e a r e a o f t h e c r y s t a l is r e l a t i v e l y l ar g e , a n dt h e r e t a r d a t i o n m o d e r a t e o r h i g h . C r y s t a ls a s p l a te s , c u t se c t io n s , o rg r a in s , a r e m o u n t e d b e t w e e n c o v e r - sl ip g la s s i n a s o l id o r l iq u i d m e d i u mi n o p t i c a l c o n t i n u i t y w i t h t h e s p h e re . T h e r e f r a c t iv e i n d e x o f t h ee m b e d d i n g m e d i u m s h o u l d p r e f e ra b l y b e n e a r t h a t o f fl f o r t h e c r y s t a l ;a n d , t o a v o i d t o t a l r e f le c t io n e ff ec ts , i t m a y b e a d v i s a b l e t o u s e m o u n t i n gm a t e r i a l s w i t h in d i c e s n e a r o r h i g h e r t h a n t h a t o f t h e s p h e re . I f n e c e s -s a r y , s p e c i a l c o v e r -s l ip s m a y h e g r o u n d f o r th e p u r p o s e f r o m h i g h r e f r a c -t i v e i n d e x g l a s s .O f t h e r a y s e n t e r i n g t h e s p he re , t h o s e w h i c h d o n o t p a s s t h r o u g h t h ec r y s t a l m a y g i v e a b a c k g r o u n d o f u n d e s i ra b l e i l l u m i n a ti o n o n t h e s c re e n ,a n d s o r e d u c e th e q u a l i t y o f t h e i m a g e . T h e y m a y b e e l im i n a t e d w h e nn e c e s s a r y b y m e a n s o f a m a s k o f f oil , w i t h a c e n t r a l o p e n i n g , a t t a c h e dt o o n e o f t h e s e g m e n t s .

T h e in s t r u m e n t is b e s t u s e d i n a d a r k e n e d r o o m . A f t e r a d j u s ti n g t h el ig h t s o u r c e f o r t h e m o s t e f f e c ti v e c o n c e n t r a t i o n , t h e i n n e r r i n g is r o t a t e dt o e x t i n c t i o n , a n d t h e s p h e r e , w i t h t h e c r y s t a l m o u n t e d a t t h e c e n t r e , i sp l a c e d i n i ts s u p p o r t . S p e c i m e n s g i v e t h e b e s t r e s u lt s w h e n th e p l a n e o fs e p a r a t io n o f t h e s e g m e n t s is n o t t o o h i g h l y t i l te d a n d w h e n t h e a c u t eb i s e c t r ix , o r a n o p t i c a x i s , is h i g h l y i n c l in e d t o t h i s p l a n e . S t r a y il lu -m i n a t i o n o n o n e s id e o f t h e s c r e e n a ri s in g w h e n t h e o r i e n t a t i o n o f t h es p e c i m e n i s u n f a v o u r a b l e s h o u l d b e s c r e e n e d o f f n e a r t h e s p h e r e .U t i l iz i n g t h e t r a n s p a r e n t s t ri p , T , t h e s p h e r e m a y b e r e v o l v e d t o d is -p l a y t h e i n te r f e r e n c e p h e n o m e n a f o r a n y d e s ir e d c r y s t a l o r i e n t a t io n .

T h e c r y s t a l m a y a l so b e re v o l v e d b y t u r n i n g t h e s ta g e , a n d b o t ha n a l y s e r a n d s c r e e n h a v e i n d e p e n d e n t r o t a t io n . T h e b e h a v i o u r o f t h ei so g y re s , a n d o t h e r e o n o s c o p ic p h e n o m e n a , m a y t h e r e f o r e b e o b s e r v e da n d d e m o n s t r a t e d f o r a n y c h o s e n o r i e n t a t io n . T h e in t e r f e r e n c e f i g u reo f a t h i c k f l a k e o f m u s c o v i t e , 2 V 4 3 ~ i s s h o w n i n f ig . 2 .

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me nt on the sc reen be tween the two opti c axes which m ay be ad jus t ed tofall upon the scale of degrees inscribed in the screen ; or a s t r ip of metalf i tt ing the curve of the sc reen and m arked in degrees m ay be usedenabl ing measurement s to bemad e a t an y pos i tion . The pr in-cipal planes and points of emer-gence of the axes of the ind ica t r ixare a l so ava i l ab le and may betemp orar i ly inscribed on thescreen if desired.

When t he r e f r ac t i ve i ndex o fthe glass compris ing the sphered if fe rs f rom tha t o f f i o f thecrys t a l cor rec t ion of the ob-served value of 2V is necessary.I f fl fo r the c rys t a l is known andalso th e gr ea t circle m ea su re m en t Fro. 2. Interference figure of muscovite.f rom each op t i c ax i s to the po la rpo in t o f emergence on the sc reen of the ax is o f the sphere perpendicu la rto the p lane of separa t ion of the segment s the t rue va lue for 2V isread i ly ava il ab le The two oppos i te po la r po in t s hav ing been mar ked onthe sphere the equiva len t sc reen-poin t ma y be loca ted and es tab li shedut i liz ing a dr op of benzine held by surface tension against the surfaceof the screen by m ean s of a glass sl ide. This acts as a lens an d alsorenders the sc reen t emp orar i ly t ransparen t enabl ing the po la r po in t son the sphere to be a ligned and the equiva len t po in t i nscr ibed on thescreen. By re fe rence to a c har t t he ame nded angular read ings a reava i lab le and m ay be ma rked off f rom the po la r po in t t hus g iv ing eachcorrec ted op t i c ax is pos i tion for measure men t o f 2V. To improve ac cura cyi n quan t i t a t i ve w ork t he sphe re m ay be r eve r sed t o ob t a i n t he m ean o ftwo sets o f readings.

For s tudies in paral le l polar ized l ight the screen i s removed and thei l luminat ion res t r ic ted to a smal l apertu re a t the ce nt re of a disk placedup on the cell. Becke-l ine observ at ions are ma de wi th a hand-lens forre f rac t ive index de te rmina t ion .

W hen m onoc hrom at i c l igh t is required the sphere m ay be i l l umina tedby a sod ium-vapour l amp or o ther source inser t ed in an opening for thepurpose in the s ide of the re f lec tor and dye d photogra phic p l a t es a reuseful as f i l ters for demonst rat ion work.