T H E D E T E R M IN A T IO N O F T H E E L A S T IC C O N S TA N TS O F O P T IC A L GLASSES B Y AN U L T R A S O N IC M E T H O D By J A M E S M IL T O N B A R N E S AN ABSTRACT S u b m itte d to th e S c h o o l o f G ra d u a te S tu d ie s o f M ic h ig a n S ta te C o lle g e o f A g r ic u lt u r e and A p p lie d S c ie n c e in p a r t i a l f u l f i ll m e n t o f th e r e q u ir e m e n ts f o r th e d e g re e o f D O C T O R O F P H IL O S O P H Y D e p a rtm e n t o f P h y s ic s 1955 Aa p p ro v e dj : ^ A '- ProQuest Number: 10008464 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 10008464 Published by ProQuest LLC (2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 T h e D e t e r m in a tio n o f th e E la s t ic C o n s ta n ts o f O p tic a l G la s s e s b y an U lt r a s o n ic M e th o d . Ja m e s M . B a rn e s A b s tr a c t T h e v a lu e s o f th e e la s t ic c o n s ta n ts o f t h ir t e e n s a m p le s o f o p t ic a l g la s s c o m m e r c ia lly p ro d u c e d in th e U n ite d S ta te s and a s a m p le o f fu s e d s i li c a w e r e c a lc u la te d f r o m the r e s u lt s o f m e a s u r e m e n ts m a d e o n th e s e s a m p le s . T h e m e th o d u s e d w a s a v a r ia t io n o f th e S c h a e fe r - B e r g m a n n u lt r a s o n ic m e th o d , * m o d ifie d to use d if f r a c t io n o f h ig h e r o r d e r s th a n th e f i r s t b y u s in g H ie d e m a n n p a tte r n s . 2 I t w a s fo u n d n e c e s ­ s a r y to c o n s id e r s im u lta n e o u s ly th e p o in t s o u rc e and s l i t s o u rc e d i f ­ f r a c t io n p a tte r n s in o r d e r to c h o o s e th o s e o f th e l a t t e r ty p e w h ic h w e r e s u ita b le f o r m e a s u r e m e n ts . T h e a c c u r a c ie s o f th e e x p e r im e n t a lly d e ­ t e r m in e d v a lu e s o f th e lo n g itu d in a l and s h e a r w a ve v e lo c it ie s w e r e 0. 13% and 0. 25% r e s p e c t iv e ly , w h ile th e a c c u r a c ie s in d e te r m in in g th e e la s t ic c o n s ta n ts w e r e a n d th e b u lk m o d u lu s , 0 0 . 5% f o r the s h e a r m o d u lu s , L a m e 's m o d u lu s , . 7% f o r P o is s o n 's r a t io , and 0 . 8 % f o r Y o u n g 's m o d u lu s . T h e v a lu e s o f th e s u r fa c e te n s io n s o f th e s a m p le s w e r e c a lc u ­ la te d u s in g th e r e s u lt s o f th e m e a s u re m e n ts and A u e r b a c h 's e q u a tio n . 3 A b s t r a c t — R e fe re n c e s 1. S c h a e fe r, C l. a n d L . B e r g m a n n , L a u e - D ia g r a m m e m i t o p tis c h e n W e lle n . B e r l i n B e r . (1 9 3 4 ) 155, N o. 10. S c h a e fe r, C l. , L . B e rg m a n n , and H . J . G o e h lic h . B e s tim m u n g d e r e la s tis c h e n K o n s ta n te n o p tis c h e r G la s e r aus d e r L ic h tb e u g u n g a n U lt r a s c h a llw e lle n . G la s te c h n . B e r . 15 , 4 4 7 -6 1 (1 9 3 7 ). 2. H ie d e m a n n , E . and K . H . H o e s c h . S c h u b w e lle n a ls o p tis c h e G it t e r . N a tu r w is s . 23_, 5 1 1 -2 (1 9 35 ), B h a g a v a n ta n , S. and B . R. R ao. H ie d e m a n n P a tte r n s a t V e r y H ig h F r e q u e n c ie s . N a tu r e (L o n d . ) 159, 742 (1 9 4 7 ). 3. A u e rb a c h , R . O b e rfla c h e n s p a n n u n g und S c h a llg e s c h w in d ig k e it. E x p e r ie n tia 4 , 4 7 3 -4 (1 9 4 8 ) N o. 12. T H E D E T E R M IN A T IO N O F T H E E L A S T IC C O N STA N TS O F O P T IC A L GLASSES B Y A N U LT R A S O N IC M E T H O D By J A M E S M IL T O N B A R N E S A T H E S IS S u b m itte d to th e S c h o o l o f G ra d u a te S tu d ie s o f M ic h ig a n S ta te C o lle g e o f A g r ic u lt u r e and A p p lie d S c ie n c e in p a r t i a l f u l f i ll m e n t o f the r e q u ir e m e n ts f o r th e d e g re e o f D O C T O R O F P H IL O S O P H Y D e p a r tm e n t o f P h y s ic s 1955 ACKNOWLEDGMENTS I w ish to e x p r e s s m y m o s t s in c e r e a p p r e c ia tio n to D r. E. A. H i e d e m a n n f o r th e in s p ir a t io n and g u id a n c e w h ic h h e lp e d to b r in g th is th e s is to a s u c c e s s fu l c o n c lu s io n . I a ls o w is h to e x p r e s s m y in d e b te d n e s s to th e O w e n s I l l i n o i s G la s s C o m p a n y f o r p r o v id in g fu n d s and a id in g i n o b ta in in g m a t e r ia ls f o r th e m e a s u re m e n ts in c lu d e d in th is p a p e r. Ja m e s M . B a rn e s T a b le o f C o n te n ts T a b le o f S y m b o ls 4 In tr o d u c tio n 5 E x p e r im e n ta l P r in c ip le 9 D e s c r ip t io n o f E x p e r im e n ta l A p p a ra tu s 29 M e a s u re m e n t P ro c e d u re 39 E x p e r im e n ta l M a t e r ia ls a n d R e s u lts 42 S u m m a ry 52 R e fe re n c e s 53 4 T A B L E 0 m, n OF SYMBOLS — D if f r a c t io n A n g le — O r d e r o f D if f r a c t io n ^ o ” O p tic a l W a ve L e n g th in A i r A l ■= L o n g itu d in a l U lt r a s o n ic W a ve L e n g th As — S h e a r U lt r a s o n ic W a ve L e n g th F — F o c a l L e n g th o f O b je c tiv e L e n s r ^ R — S h e a r W a ve D if f r a c t io n P a tte r n S p a c in g f ~ L o n g itu d in a l W ave D if f r a c t io n P a tt e r n S p a c in g F r e q u e n c y o f th e U lt r a s o n ic W ave VL — L o n g itu d in a l W ave V e lo c it y V5 ~ S h e a r W ave V e lo c it y X p — L a m e ’ s E la s t ic M o d u lu s =■ S h e a r E la s t ic M o d u lu s k =• B u lk E la s t ic M o d u lu s E = Y o u n g 's E la s t ic M o d u lu s C = P o is s o n 's R a tio f o r the E la s t ic M e d iu m p — D e n s ity o f th e M e d iu m d = C o m p a r is o n G r a tin g C o n s ta n t x — C o m p a r is o n G r a tin g D if f r a c t io n P a tte r n S p a c in g S — S u rfa c e T e n s io n o f th e M e d iu m 5 I n t r o d u c tio n T h e o b je c t o f th e s tu d y r e p o r t e d in t h is p a p e r w a s th e d e t e r ­ m in a t io n o f th e e la s t ic c o n s ta n ts o f a s e r ie s o f o p tic a l g la s s e s b y a m e th o d u s in g th e d if f r a c t io n o f lig h t p ro d u c e d b y e la s t ic w a v e s o f h ig h u lt r a s o n ic fre q u e n c y . In 1932 P . D e b y e and F . W . S e a rs * in A m e r ic a and R. L u c a s 2 a n d P . B iq u a r d in F r a n c e d is c o v e r e d s im u lta n e o u s ly and in d e p e n d ­ e n tly th a t u lt r a s o n ic w a v e s c a n a c t as o p tic a l d if f r a c t io n g r a tin g s . I f a n u lt r a s o n ic w a v e is e x c ite d in a tr a n s p a r e n t m e d iu m and i f lig h t p a s s e s th r o u g h i t in a d ir e c t io n p e r p e n d ic u la r to th e d ir e c t io n o f p r o p a ­ g a tio n o f th e a c o u s tic a l w a v e , a d if f r a c t io n p a tte r n o f th e lig h t is fo r m e d r e s e m b lin g th a t o b ta in e d b y m e a n s o f a s im p le lin e g r a tin g . The g ra t­ in g s p a c in g c o r r e s p o n d s to th e le n g th o f th e s o u n d w a v e in th e m e d iu m . T h e use o f h ig h u lt r a s o n ic fre q u e n c ie s a llo w s one to o b ta in th e c o n d i­ t io n f o r an " i n f i n i t e " m e d iu m w it h r a t h e r s m a ll s a m p le s . I t is o n ly n e c e s s a r y th a t th e d im e n s io n s o f th e s a m p le a re la r g e c o m p a re d w it h th e w a ve le n g th . In th e c a s e o f an " i n f i n i t e " is o t r o p ic s o lid th e r e e x is t o n ly tw o ty p e s o f e la s t ic w a v e s in th e m e d iu m , n a m e ly th e lo n g itu d in a l and th e s h e a r w a v e s . I f th e d e n s ity o f th e m e d iu m is k n o w n , th e tw o e la s t ic c o n s ta n ts o f an id e a l is o t r o p ic s o lid c a n be c o m p u te d f r o m th e v e lo c it ie s 6 o f p r o p a g a tio n o f th e tw o ty p e s o f w a v e s . T o d e te r m in e th e v e lo c it y o f p r o p a g a tio n o f a w a v e one o fte n m e a s u re s b o th fr e q u e n c y and w a v e le n g th . T h e fr e q u e n c y o f u lt r a s o n ic w a v e s c a n be o b ta in e d w it h ease f r o m th e m e a s u r e m e n t o f th e fr e q u e n c y o f th e e le c t r ic a l c i r c u i t d r i v ­ in g th e tr a n s d u c e r . T h e m a in p r o b le m is th e r e fo r e th e m e a s u re m e n t o f th e w a v e le n g th . T h e d if f r a c t i o n o f lig h t b y u lt r a s o n ic w a v e s o ffe r s v a r io u s p o s ­ s i b i l i t i e s f o r th e m e a s u r e m e n t o f th e u lt r a s o n ic w a ve le n g th . Two d if f e r e n t m e th o d s h a ve b e e n u s e d f o r s y s te m a tic s tu d ie s o f th e e la s t ic c o n s ta n ts o f o p tic a l g la s s e s . C l. S c h a e fe r, L . B e rg m a n n , and H . J . 3 G o e h lic h te r n s . 4 u s e d th e m e th o d o f th e S c h a e fe r -B e r g m a n n d if f r a c t io n p a tK . H. H oesch 5 u se d a m e th o d o f E . H ie d e m a n n ® c o n s is tin g o f d ir e c t m e a s u r e m e n t o f th e w a v e le n g th o f th e tw o d if f e r e n t w a v e s . S c h a e fe r, B e r g m a n n , and G o e h lic h r e p la c e d th e s l i t in th e u s u a l D e b y e -S e a rs a r r a n g e m e n t b y a s m a ll c i r c u l a r a p e r tu r e . T h e lig h t p a s s in g th r o u g h th e g la s s s a m p le w a s s lig h t ly c o n v e rg e n t, th e im a g e o f th e s o u rc e b e in g fo c u s e d on a p h o to g ra p h ic f i l m a p p r o x im a te ly one m e t e r d is ta n t f r o m th e s a m p le . T h e s p a c in g o f th e o r d e r s on th e f i l m to g e th e r w it h th e c o n s ta n ts o f th e o p tic a l s y s te m s u ffic e d to d e te r m in e th e u lt r a s o n ic w a v e le n g th in th e g la s s . In is o t r o p ic m e d ia th e S c h a e fe r - B e r g m a n n p a tte r n s a re o f th e c i r c u l a r fo r m . A s t h e i r g la s s s a m p le s w e r e c u b e s and the u lt r a s o n ic v ib r a t io n s w e r e e x c ite d b y m e a n s o f an X - c u t q u a r tz fa s te n e d to one s u r fa c e , r e f le c t io n s o f the 7 s id e lo b e s o f th e u lt r a s o n ic b e a m a t th e s u r fa c e s o f th e cu b e c o m b in e d w it h in t e r n a l c o u p lin g c a u s e d th e w a v e s to f i l l th e b lo c k w it h th e w a v e s b e in g p ro p a g a te d in m a n y d ir e c t io n s . E a c h w a v e p r o p a g a tio n d ir e c t io n w h ic h w a s n o r m a l to th e a x is o f th e o p tic a l s y s te m p ro d u c e d a p a ir o f d ia m e t r ic a lly o p p o s ite d if f r a c t io n p o in ts . D ue to th e p re s e n c e o f b o th s h e a r and lo n g itu d in a l w a v e s th e l o c i o f th e d if f r a c t io n p o in ts w e r e tw o c o n c e n tr ic c i r c le s a ro u n d th e c e n t r a l im a g e p o in t. E a c h c i r c le c o r ­ re s p o n d e d to one o f th e tw o ty p e s o f w a v e s — th e la r g e r one to th e s h e a r w a v e s . T h e s p a c in g o f th e o r d e r s w a s fo u n d b y m e a s u r in g th e d ia m e te r s o f th e c i r c le s . S c h a e fe r, B e r g m a n n , and G o e h lic h c a lib r a te d t h e i r o p tic a l s y s te m b y p la c in g a p la n e g r a tin g ju s t in f r o n t o f th e g la s s cube and c o r r e c t ­ in g f o r th e d iffe r e n c e o f p o s itio n b e tw e e n i t and th e u lt r a s o n ic g r a tin g , w h ic h th e y p r o v e d to e x is t a t e s s e n t ia lly th e c e n te r o f th e cube. H o e s c h to o k c a r e to l i m i t th e p re s e n c e o f th e s ta tio n a r y w a v e s to one d ir e c t io n o n ly . T h e d if f e r e n t ty p e s o f w a v e s w e r e o b s e rv e d s e p a ­ r a t e l y b y m e a n s o f u s in g th e e x p e r im e n ta l p ro c e d u r e s o f p h o to - e la s tic a n a ly s is . 7 H o e s c h m e a s u r e d th e s ta n d in g w a v e p a tte r n d ir e c t ly th ro u g h a m ic r o s c o p e h e ld o n a t r a v e r s e m o u n t d r iv e n b y a m ic r o m e t e r s c r e w . In th is m a n n e r a d ir e c t m e a s u re m e n t o f th e u lt r a s o n ic g r a tin g w as m a d e o v e r a la r g e n u m b e r o f g r a tin g s p a c e s . T h e m e th o d w a s v e r y a c c u r a te , b u t i t r e q u ir e d s o m e tim e . I t a p p e a re d p o s s ib le th a t th e a c c u r a c y o f m e a s u r in g th e d if f r a c ­ tio n a n g le s w o u ld be in c r e a s e d b y u s in g th e s h a r p im a g e s o f a s l i t 8 in s te a d o f th o s e o f a c i r c u l a r a p e r tu r e . T h e d if f r a c t io n p a tte r n p r o ­ d u c e d b y th e g r a tin g c o u ld h a v e b e e n m e a s u r e d b y a t r a v e r s in g m ic r o s c o p e . T h e a u th o r, h o w e v e r, d e c id e d th a t a m e a s u r in g m e th o d in v o lv in g a p e rm a n e n t r e c o r d w a s m o r e s a t is f a c t o r y and th a t th e use g o f a lin e d if f r a c t io n s p e c tr u m a ls o c a lle d th e H ie d e m a n n p a tte r n , c o u ld p ro d u c e g r e a t e r p r e c is io n b y th e u se o f h ig h e r o r d e r s . 9 E x p e r im e n t a l P r in c ip le T h e p r in c ip le o f th is e x p e r im e n t fo llo w s c lo s e ly th e o r ig i n a l a r ­ ra n g e m e n t o f D e b y e and S e a rs o r L u c a s and B iq u a r d r e s p e c t iv e ly . A g la s s c u b e w a s e x c ite d in to v ib r a t io n b y m e a n s o f a p ie z o - e le c t r ic q u a r tz p la te a tta c h e d to one fa c e . * T h e v ib r a t io n s in th e m e d iu m w e r e in th e f o r m o f s ta n d in g w a v e s o f th e s a m e fr e q u e n c y as th a t o f th e v o lta g e a p p lie d to th e q u a r tz . P a r a lle l lig h t p a s s in g th r o u g h th e b lo c k in a d ir e c t io n p a r a l l e l to th e fa c e o f th e q u a r tz p la te w a s d i f ­ f r a c t e d b y th e u lt r a s o n ic w a v e s y s te m a n d fo c u s e d o n a s c r e e n o r p h o to g r a p h ic p la te . F ig . 1 sh o w s th e r e la t io n s h ip b e tw e e n th e v a r io u s d ir e c t io n s a t the g la s s b lo c k . T h o u g h th e s y s te m o f s ta n d in g w a v e s m a y b e c o m e v e r y c o m p lic a te d due to th e r e f le c t io n s f r o m th e s u r fa c e s a n d in t e r n a l c o u p lin g , i t w a s g e n e r a lly p o s s ib le to a d ju s t th e fre q u e n c y s u c h th a t m o s t o f th e u lt r a s o n ic e n e rg y la y in th o s e w a v e s w h o s e p r o p ­ a g a tio n d ir e c t io n w a s p e r p e n d ic u la r to th e fa c e o f th e cube to w h ic h th e d r iv in g q u a r tz w a s a tta c h e d . . W h e n t h is o c c u r r e d , th e in t e r fe r e n c e p a tte r n , h e r e in a f t e r r e f e r r e d to a s th e d if f r a c t io n p a tte r n , h a d th e m a x im u m n u m b e r o f o r d e r s . T h e th e o r y o f th e d if f r a c t io n due to e it h e r th e lo n g itu d in a l o r s h e a r u lt r a s o n ic w a v e s has b e e n g iv e n b y * T h e w a v e s y s te m p ro d u c e d in th e g la s s d e pends a ls o o n th e ty p e o f a c o u s tic a l c o n ta c t. C e m e n tin g th e q u a r tz to th e s a m p le g e n e r a lly fa v o r s th e S c h a e fe r - B e r g m a n n p a tte r n s . ^ CO LU Q O 0 a: o UJ ^ ASSEMBLY o ID a: CO t— < t Q Fl&.l. DETAIL OF GLASS BLOCK < o UJ ac o o _I CD Q_ O a: o NJ 1— CO CO CSL —I ZD < - cb < O 11 H . M u e lle r ’ ^ * and N . S. N . N a th and H . M u e ll e r ^ . A v e ry illu m i­ n a tin g t h e o r e t ic a l e x p la n a tio n w a s g iv e n b y S c h a e fe r, B e r g m a n n , a n d 3 G o e h lic h . T h e ty p e o f s o u rc e a p e r tu r e u se d d e te r m in e s th e ty p e o f d i f ­ f r a c t io n p a tte r n o b ta in e d . A p o in t s o u rc e c o n s is tin g o f a s m a ll ro u n d a p e r t u r e w i l l p ro d u c e a d if f r a c t io n p a tte r n c o n s is tin g o f a s e t o f p o in ts o f lig h t . lin e s . A s l i t s o u r c e p ro d u c e s a p a tte r n w h ic h is a s e t o f p a r a lle l E a c h ty p e o f s o u rc e has it s a d v a n ta g e . T h e d if f r a c t e d p o in ts o f a p o in t s o u rc e l ie a lo n g a s tr a ig h t lin e p a s s in g th r o u g h th e c e n t r a l o rd e r. T h e d ir e c t io n o f th is lin e is th e d ir e c t io n o f p ro p a g a tio n o f th e p a r t i c u l a r w a v e w h ic h is c a u s in g th e d if f r a c t io n . I f m o r e th a n one s ta n d in g w a v e o f s u f f ic ie n t in t e n s ity to p ro d u c e d if f r a c t io n o c c u r s w it h in th e g la s s c u b e , th e re w i l l o c c u r s e v e r a l lin e s o f p o in ts o f e q u a l s p a c in g b u t w it h d if f e r e n t d ir e c t io n s d e p e n d in g on th e d ir e c t io n o f th e d if f r a c t in g u lt r a s o n ic w a v e . W ith enough o f th e s e w a v e s in d if f e r e n t d ir e c t io n s one o b ta in s the c h a r a c t e r is t ic S c h a e fe r -B e r g m a n n c i r c u l a r d if f r a c t io n p a tte r n s . A s l i t s o u rc e m a y be c o n s id e re d as a la r g e n u m b e r o f p o in t s o u rc e s s e t a lo n g in a r o w . E a c h d if fr a c te d p o in t a s d e s c r ib e d in the p r e c e d in g p a r a g r a p h b e c o m e s a d if f r a c t e d lin e . O b v io u s ly a s e t o f s ta n d in g w a v e s w h ic h p ro d u c e s a go od S c h a e fe r -B e r g m a n n p a tte r n w i l l p ro d u c e a h o p e le s s c o n fu s io n o f lin e s w it h a s l i t s o u rc e . F ig . 2, a p h o to g ra p h ta k e n w h e n a p o in t s o u rc e and a lin e s o u rc e w e r e u s e d FIG. 2. PHOTOGRAPH OF A SIMULTANEOUS SCHAEFERBERGMANN POINT SOURCE DIFFRACTION PATTERN AND A LINE DIFFRACTION PATTERN SHOWING HOW THE POINTS ON THE LONGITUDINAL WAVE (INNER) AND SHEAR WAVE IOUTERI CIRCLES PRODUCE POORLY DEFINED AND SPACED LINES W H IC H ARE UNSUITABLE FOR MEASUREMENT 13 s im u lta n e o u s ly , i ll u s t r a t e s th is c a s e . ( F ig . 2 w a s ta k e n in th e fu s e d s i l i c a s a m p le a t an u lt r a s o n ic fr e q u e n c y o f 11. 748 m c / s e c . ) H o w e v e r, a s l i t s o u r c e h a s th e a d v a n ta g e th a t i t m a y e a s ily be a d ju s te d f o r s iz e , s o m e th in g w h ic h is n o t p r a c t ic a l f o r s m a ll c i r c u l a r a p e r tu r e s . Thus f o r t h is in v e s t ig a tio n a s l i t s o u rc e w a s u s e d in o r d e r to o b ta in as fin e a d if f r a c t i o n p a tte r n as p o s s ib le . T h e a d v a n ta g e o f a p o in t s o u rc e w a s u s e d to a v o id m is ta k e s due to " a p p a r e n t" d if f r a c t io n lin e s . In e v a lu a tin g a d if f r a c t io n p h o to g ra p h to d e te r m in e w h e th e r o r n o t i t is w o r t h p u ttin g th r o u g h th e m e a s u r in g p r o c e s s , one m u s t k n o w i f th e p e r p e n d ic u la r d is ta n c e b e tw e e n th e lin e s is a tr u e in d ic a tio n o f th e e ffe c t one w is h e s to m e a s u re . R e f e r r in g a g a in to F ig . 2, one c a n see th a t no m e a s u r e m e n t b e tw e e n lin e s c o u ld be in d ic a tiv e o f th e tr u e lo n g itu d in a l d if f r a c t io n p a tte r n s p a c in g . In c o n tr a s t, c o n s id e r th e tw o p a r t s o f th e p h o to g ra p h s h o w n in F ig . 4. A lth o u g h th is p h o to g ra p h is p r e s e n te d p r i m a r i l y to illu s t r a t e a d if fe r e n t p h e n o m e n o n , n o te th a t the p a tte r n f r o m th e p o in t s o u rc e c o n s is ts o f a lin e o f d o ts , a n d th a t a t b e s t o n ly a fe w d im p o in ts r e m a in o f a c i r c u l a r p a tte r n . A ls o n o te th a t as f a r as b r ig h tn e s s o f th e p a tte r n a llo w e d , th e r e is a lin e f o r e v e r y p o in t and th e s p a c in g b e tw e e n lin e s c o rr e s p o n d s to th e s p a c in g b e tw e e n p o in ts . In g e n e r a l in th e m e a s u re d p h o to g ra p h s th e r e w e r e no m o r e d o ts v is ib le th a n th e r e w e re lin e s , and th e lin e s , b y n a tu r e o f th e s l i t u s e d , h a d v a r y in g w id th s so th a t a p o s itio n c o u ld be fo u n d w h ic h a llo w e d o p tim u m a c c u r a c y o f s e ttin g o f th e m e a s u r in g in s t r u m e n t 14 used. In a l l c a s e s , th e n , th e s o u r c e u s e d h a d a c o m b in a tio n o f a p o in t o p e n in g a n d a s l i t o p e n in g o f v a r y in g w id th . F o r a l l m e a s u r e m e n ts d i f ­ f r a c t i o n p a tte r n s w e r e s e a rc h e d f o r in w h ic h th e d if f r a c t io n p a tte r n f r o m th e p o in t p a r t o f th e s o u rc e c o n s is te d o f a lin e o f d o ts p e r p e n d ic u ­ l a r to th e q u a r tz p la te (a n d th u s p e r p e n d ic u la r to th e s lit ) . B y v a r y in g th e fre q u e n c y one c o u ld w a tc h th e p a tte r n s o f th e s ta n d in g w a v e s change u n t i l a p a tte r n o f th e d e s ir e d c o n fig u r a tio n w a s fo u n d . W ith s o m e g la s s s a m p le s i t w a s im p o s s ib le to f in d the d e s ir e d p a tte r n s w it h in c e r t a in o f th e fr e q u e n c y ra n g e s u s e d . W ith b o th th e p o in t p a tte r n and th e lin e p a tte r n s h o w in g on th e fin is h e d p h o to g ra p h , a p e rm a n e n t r e c o r d w a s o b ta in e d o f th e p a tte r n to g e th e r w it h it s g e n e ra tin g p o in t c o n fig u ­ r a t io n . O n e a ch p la te th e r e a ls o a p p e a re d a r e c o r d o f th e p a tte r n due to th e c a lib r a t io n g r a tin g ( e x p la in e d f a r t h e r o n ) so th a t p o s s ib ilit ie s o f ch a n g e due to e m u ls io n s h rin k a g e o r o th e r e ffe c ts w e re m in im iz e d . A lth o u g h i t w a s p o s s ib le to ta k e d if f r a c t io n p ic t u r e s w ith o u t th e m , th e a d d itio n o f a p o la r iz e r a n d an a n a ly z e r , one on e it h e r s id e o f th e g la s s b lo c k , a llo w e d in c r e a s e d s e le c t iv it y o f th e ty p e o f p a tte r n to be r e c o r d e d . T h e n a tu r e o f th e s tr a in s due to th e lo n g itu d in a l o r th e s h e a r w a v e in th e b lo c k w a s s u c h th a t p la n e - p o la r iz e d lig h t p a s s in g th r o u g h th e g la s s s p e c im e n e m e rg e d w it h a ch a ng e in p o la r iz a t io n d e ­ p e n d in g o n w h e th e r th e d if f r a c t io n o r d e r s w e r e due to th e one o r th e g o th e r ty p e o f w a v e . F o r a s p e c if ic c a s e , c o n s id e r a lo n g itu d in a l and 15 a s h e a r w a v e in th e g la s s , e a c h w it h th e s a m e , s a y v e r t i c a l, d ir e c t io n o f p ro p a g a tio n . W ith th e p o la r iz e r and a n a ly z e r p a r a l l e l and p e r p e n ­ d ic u la r to th e p r o p a g a tio n d ir e c t io n ( c r o s s e d w it h one a n o th e r ) , o n ly th e s h e a r w a v e d if f r a c t io n p a tte r n is o b s e rv e d . W ith th e p o la r iz e r a n d a n a ly z e r s t i l l c r o s s e d , b u t e a c h m a k in g an a n g le o f 4 5 ° w it h th e p r o p a g a tio n d ir e c t io n , o n ly th e lo n g itu d in a l o r d e r s a re o b s e rv e d . In a s ­ m u c h as th e lo n g itu d in a l o r d e r s w e r e g e n e r a lly m u c h b r ig h t e r th a n th o s e due to th e s h e a r w a v e , th e p a r a lle l and p e r p e n d ic u la r a r r a n g e m e n t w a s a lm o s t a n e c e s s ity f o r o b s e r v in g and p h o to g ra p h in g th e la t t e r . In a d d itio n th e b r ig h tn e s s o f th e c e n tr a l o r d e r w a s g r e a t ly d im in is h e d , a n d s c a tte r e d lig h t a r is in g f r o m th e v a r io u s e le m e n ts o f th e o p tic a l s y s te m w a s e lim in a te d . T h e s p a c in g o f th e d if f r a c t e d lin e s in th e c a s e w h e r e th e s l i t w a s p e r p e n d ic u la r to th e u lt r a s o n ic w a ve p ro p a g a tio n d ir e c t io n w a s a fu n c tio n o f th e le n g th o f th e s ta n d in g w a ve in th e g la s s as w e ll as o f th e c o n s ta n ts o f th e o p t ic a l s y s te m . T h e s e w a v e s a c te d as a g r a tin g to d if f r a c t th e lig h t in to one o r m o r e o r d e r s . S in ce th e s p a c in g o f th e 0 u lt r a s o n ic g r a tin g w a s one w a v e le n g th , th e a n g le o f th e n ^ o r d e r o f d if f r a c t io n is g iv e n b y th e w e ll- k n o w n r e la t io n /( i1v) ft sm o = n A w h e re A© is th e o p tic a l w ave, le n g th in a i r and le n g th in th e m e d iu m . A I f a le n s o f fo c a l le n g th is th e u lt r a s o n ic w a v e F is u s e d to fo c u s th e 16 d if f r a c t i o n p a tte r n o n th e f i l m p la n e , th e s p a c in g r b e tw e e n th e z e r o o r c e n t r a l o r d e r and th e n ^ o r d e r is g iv e n b y (2 ) r — F n F >> r * A R e c o g n iz in g th a t th e r e w e r e tw o w a v e s o f d iffe r e n tw a v e le n g th s p r o ­ d u ce d in th e g la s s , th is la s t e q u a tio n ta k e s the fo llo w in g f o r m s (3 a ) F n R A© As (3 b ) F n r A, a l w h e re R is th e s h e a r w a v e d if f r a c t io n s p a c in g , n a l w a v e d if f r a c t io n s p a c in g , r is th e lo n g it u d i­ A j is the s h e a r w a v e le n g th , and A L is th e lo n g itu d in a l w a v e le n g th o f th e u lt r a s o n ic w a v e in th e g la s s . S in ce th e u lt r a s o n ic w a v e le n g th s a r e th e u n kn o w n q u a n titie s , th e e q u a tio n s a r e m o r e u s a b le in th e fo llo w in g f o r m : <4a) A s= (4 b ) A Fn R Ap F n A© r I W ith th e u se o f a c o m p a r is o n g r a tin g th e a c tu a l c a lc u la tio n o f th e v e lo c it y w a s m u c h s im p lif ie d . If x is th e s p a c in g b e tw e e n th e c e n tr a l a n d th e m ^ o r d e r o f th e c o m p a r is o n g r a tin g d if f r a c t io n p a tte r n , ta k e n w it h e x a c tly th e s a m e o p tic a l b e n c h a r r a n g e m e n t e x c e p t w it h th e g r a t ­ in g a t th e g la s s b lo c k p o s itio n , and i f g r a tin g , th e n d is th e c o n s ta n t o f th is 17 (5 ) x _ F m X C o m b in in g th is la s t e q u a tio n w it h th e tw o p r e c e d in g e q u a tio n s , one e lim in a t e s th e p r o d u c t d x M (6 ) F A 0 and has _ “ r n Aj _ R — As n o r s e p a r a te ly (7 a) . = d x n r m — d x n R m I (7 b ) A,'S K n o w in g th e fr e q u e n c y f o f th e u lt r a s o n ic w a v e s , th e v e lo c it ie s o f th e w a v e s in th e g la s s s a m p le a re g iv e n b y <8 a ) Vs = 1A (8 b) VL f A l - s w h e re V 5 is th e s h e a r w a v e v e lo c it y and is th e lo n g itu d in a l w a v e v e lo c it y . F r o m e la s t ic th e o r y th e depe n d e nce o f th e s h e a r and lo n g it u d i­ n a l v e lo c it ie s on th e e la s t ic c o n s ta n ts o f th e m e d iu m is g iv e n b y s e v ­ e r a l s im p le e q u a tio n s . T h e v a lu e s o f th e e la s tic c o n s ta n ts f o r t h is p a p e r w e re c a lc u la te d f r o m th e fo llo w in g : 18 (0) ylr =* p\J$ ( 10) A = p k = °* - E = (U) - 2^r * 4 /3 y u A A + JO ) ( 12) <13> w h e re yu m o d u lu s , is th e s h e a r m o d u lu s , E is Y o u n g 's m o d u lu s , th e d e n s ity o f th e g la s s . 2 2( 2//(l A a +a) is L a m e 's m o d u lu s , k is th e b u lk is P o is s o n 's r a t io , and p is S u rfa c e T e n s io n In 1948 R. A u e r b a c h 1 S p u b lis h e d a p a p e r in w h ic h an e m p i r i ­ c a l r e la t io n w a s g iv e n , good f o r g a s e s , liq u id s , o r s o lid s , f o r th e s u r fa c e te n s io n in t e r m s o f th e d e n s ity and th e s o u n d v e lo c it y . In a s ­ m u c h a s th e d e n s itie s and s o u n d v e lo c it ie s o f th e v a r io u s g la s s e s w e r e m e a s u r e d f o r t h is p a p e r, i t is a p p r o p r ia te th a t A u e r b a c h 's r e ­ la t io n be g iv e n a n d th e s u r fa c e te n s io n o f e a ch g la s s s a m p le c a lc u la te d If S is th e s u r fa c e te n s io n in d y n e s p e r c e n tim e t e r , t h is r e la t io n is (14) S= 6. 30 x 10"4 V 3/2 / ) w h e re th e v e lo c it y u s e d w o u ld be th e lo n g itu d in a l v e lo c it y in m e te r s p e r s e c o n d and th e d e n s ity w o u ld be in g r a m s p e r c u b ic c e n tim e te r . 20 M u lt ip le D if f r a c t i o n T h e p h e n o m e n o n o f m u lt ip le d if f r a c t io n b y u lt r a s o n ic w a v e s w a s a lr e a d y c o n s id e r e d in th e th e o r y o f C . V . R a m a n a n d N . S. N . N a th 14 . D u e to th e f i n it e th ic k n e s s o f an u lt r a s o n ic g r a tin g , lig h t d if f r a c t e d a f t e r p a s s in g th r o u g h p a r t o f th e u lt r a s o n ic g r a tin g w i l l be d if f r a c t e d a g a in b y th e s u c c e e d in g p a r ts o f th e g r a tin g . M u lt ip le d i f ­ f r a c t io n in c r e a s e s w it h th e le n g th o f the o p tic a l p a th in th e u lt r a s o n ic g r a t in g a n d w it h th e in t e n s it y o f th e w a v e s . R a m a n and N a th e x ­ p la in e d in th is w a y th e fr e q u e n c y d is t r ib u t io n o v e r th e s u b c o m p o n e n ts o f a d if f r a c t io n lin e ; e a c h s u c c e s s iv e d if f r a c t io n p ro d u c e s a D o p p le r e ffe c t to th e a m o u n t f. T h e e ffe c ts o f m u lt ip le d if f r a c t io n p ro d u c e d b y tw o u lt r a s o n ic w a v e s o f d iffe r e n tw a v e le n g th s w e r e f i r s t o b s e rv e d b y L . B e r g m a n n and E . F u e s 15 . A r ig o r o u s th e o r y o f th e m u lt ip le d if f r a c t io n b y u lt r a s o n ic w a v e s in s o lid s w a s g iv e n b y N . S. N . N a th 16 M u lt ip le d if f r a c t io n b y m e a n s o f u lt r a s o n ic w a v e s o f d if fe r e n t w a ve le n g th s g iv e s r i s e to th e a p p e a ra n c e o f a d d itio n a l d if f r a c t io n lin e s . T h e s e a d d itio n a l o r " c o m b in a t io n " lin e s and t h e i r p r o d u c tio n w i l l n o w b e d e s c r ib e d in d e t a il f o r th e s p e c ia l ca se o f g la s s . In th e g la s s b lo c k tw o s im u lta n e o u s g r a tin g s a re p ro d u c e d , one b y e a c h th e s h e a r and th e lo n g itu d in a l w a ve . T h e s e g r a tin g s a r e th ic k , th a t is , th e y m a y o c c u p y up to an in c h o f sp a ce a lo n g th e o p tic a l p a th , a n d th e y a r e in t e r m in g le d . T h u s th e r e is a m p le o p p o r tu n ity f o r m u lt ip le d if f r a c t io n to o c c u r . A s an e x a m p le , lig h t d if f r a c t e d in to th e 21 f i r s t lo n g itu d in a l o r d e r m a y be r e d if f r a c t e d b y th e s h e a r w a v e g r a tin g in to a p lu s o r m in u s f i r s t s h e a r o r d e r w it h th e lo n g itu d in a l o r d e r as c e n tra l o rd e r. O ne m a y ju s t as e a s ily c o n s id e r th e lo n g itu d in a l and s h e a r g r a tin g r o le s to b e in te rc h a n g e d in th e la s t s ta te m e n t. In a s ­ m u c h as th e s h e a r w a v e u n d e r n o r m a l c o n d itio n s n e v e r p ro d u c e s an o r d e r h ig h e r th a n th e f i r s t * * , i t is m o r e c o n v e n ie n t to c o n s id e r th e s h e a r d if f r a c t io n as th e f i r s t d if f r a c t io n , fo llo w e d b y th e lo n g itu d in a l d if f r a c t io n . In o r d e r to u n d e rs ta n d ho w th e m u lt ip le d if f r a c t io n p a tte r n d e ­ v e lo p s , F ig . 3 has been p re p a re d . T h e p a r ts o f th is f ig u r e a re d i f ­ f r a c t io n p a tte r n p h o to g ra p h s ta k e n a t th e sa m e fre q u e n c y ( f = 11, 973 m c / s e c . ) in th e s a m e m a t e r ia l (B a u s c h a n d L o m b g la s s ty p e L F - 1 ) w it h o n ly th e in t e n s it y o f th e u lt r a s o n ic s ta n d in g w a v e p a tte r n ** T h is w a s e x p la in e d b y H . M u e lle r o f E . H ie d e m a n n and K . H . H o e s c h 17 10 . in c o r r e la t io n w it h th e r e s u lt s .. 18 R o tg e r has sh o w n th a t i t is p o s s ib le to in c r e a s e th e in t e n s ity o f th e s h e a r w a v e s enough to o b ta in th e s e c o n d d if f r a c t io n o r d e r . H e u se d a g la s s b lo c k o f t r ia n g u la r c r o s s - s e c t io n ; u lt r a s o n ic w a v e s e n te r in g th ro u g h one fa c e o f th e b lo c k w e r e r e fle c te d a t th e n e x t fa c e u n d e r an a n g le fa v o r in g o p tim u m p r o ­ d u c tio n o f s h e a r w a v e s . FIG. 3. A SET OF PHOTOGRAPHS OF ULTRASONIC DIFFRACTION PATTERNS TAKEN AT THE SAME FREQUENCY IN THE SAME GLASS SAMPLE, SHOW ING THE EFFECT OF INCREASING THE ENERGY IN THE ULTRA­ SONIC STANDING WAVE IN THE BLOCK. THE CHANGES IN LINE WIDTH ARE DUE TO DIFFERENT EXPOSURE TIMES. A. LOW ULTRASONIC INTENSITY B. MEDIUM ULTRASONIC INTENSITY C. HIGH ULTRASONIC INTENSITY 23 changed. P a r t A w a s ta k e n a t lo w e x c it a tio n in t e n s it y * ^ * . It show s th e s im p le s t d if f r a c t io n p a tte r n o b ta in a b le w it h th e tw o w a v e s p r e s e n t in th e s a m p le . T h e in n e r p a ir o f lin e s is th e f i r s t o r d e r o f th e lo n g i­ tu d in a l d if f r a c t io n p a tte r n , a n d th e o u te r p a ir is th e f i r s t o r d e r o f th e s h e a r d if f r a c t io n p a tte r n . P a r t B is a p h o to g ra p h ta k e n at m e d iu m u lt r a s o n ic in t e n s ity a n d s h o w s , b e s id e s th e o r d e r s o f p a r t A , th e a p p e a ra n c e o f th e s e c o n d o r d e r s o f th e lo n g itu d in a l w a v e a n d th e fo u r lin e s w h ic h a r e th e f i r s t m u lt ip le d if f r a c t io n lin e s . f r o m th e c e n t r a l o r d e r . T h e s e lin e s a r e th e f i r s t and la s t lin e s o u t T h e y m a y be g ro u p e d in s y m m e t r ic a l p a ir s u s in g th e f i r s t o r d e r s o f e it h e r th e lo n g itu d in a l o r s h e a r w a v e p r im a r y p a tte r n s as t h e i r c e n t r a l o r d e r s . O n f u r t h e r in c r e a s in g th e u lt r a s o n ic in te n s ity , th e o r d e r s a d d e d to th e a b ove in p a r t C a r e th e t h i r d o r d e r s o f th e lo n g itu d in a l w a v e p a tte r n and f o u r m o r e lin e s due to m u lt ip le d if f r a c t io n . C o n s id ­ e r in g th e p r im a r y s h e a r o r d e r s as c e n tr a l o r d e r s f o r m u lt ip le d i f f r a c ­ tio n , e a c h h a s a p a tte r n o f tw o o r d e r s o f lo n g itu d in a l s p a c in g a b o u t it . In g e n e r a l, i f th e lo n g itu d in a l w a v e d if f r a c t s th e lig h t in to n th e s h e a r o r d e r is r e la t iv e l y s tr o n g , th e re s h o u ld be v is ib le o r d e r s and n o rd e rs * * * F o r c o m p a r is o n , th e v o lta g e a p p lie d to th e p la te o f th e f in a l p o w e r a m p li f i e r f o r th is p a r t w a s 150 v o lt s , f o r p a r t B a b o u t 300 v o lt s , and f o r p a r t C a b o u t 800 v o lt s . 24 o f p r i m a r y lo n g itu d in a l d if f r a c t io n , f r a c t io n , and o rd e r. 2 1 o r d e r o f p r im a r y s h e a r d i f ­ n o r d e r s o f m u lt ip le d if f r a c t io n , p lu s th e c e n t r a l Thus fo r n = 5, 33 lin e s s h o u ld be v is ib le . le a s t on th e o r ig i n a l n e g a tiv e , h a d th is m a n y lin e s . F ig . 4 , at T h e m u lt ip le p r o c e s s e s o f p h o to g r a p h ic r e p r o d u c tio n n e c e s s a r y f o r p r e p a r in g th e f ig u r e s m a y re d u c e th e d e f in itio n o f th e p ic t u r e . F ig . 4 h a s b e e n p r e p a r e d to f u r t h e r c l a r i f y th e g ro u p in g a r ­ ra n g e m e n t o f a m u lt ip le d if f r a c t io n p a tte r n . B o th th e lin e a n d th e p o in t s o u r c e p a tte r n h a v e b e e n in c lu d e d to sh o w th e r e la t io n s h ip o f one to th e o th e r . T h e p h o to g ra p h w a s ta k e n in th e B a u s c h and L o m b ty p e D B F - 1 g la s s s a m p le a t a fr e q u e n c y o f 10. 019 m c /s e c . T h in lin e s h a v e b e e n e x te n d e d d o w n f r o m th e p h o to g ra p h , a n d s u p e rim p o s e d o n th e s e lin e s a re th e g ro u p in g p a tte r n s in h e a v y lin e s f o r b o th p r im a r y s e ts o f o r d e r s and th e tw o m u lt ip ly d if fr a c te d s e ts o f o r d e r s . I f th e o r d e r s a r e n o t v is ib le in th e lin e s p e c tr u m , th e y a re c e r t a in ly v i s ib l e in th e p o in t d if f r a c t io n s p e c tr u m , w h e re th e a u th o r c o u n te d e n o u g h p o in ts o f lig h t on th e o r ig in a l n e g a tiv e to have g e n e ra te d 45 lin e s . O b s e r v a tio n o f n u m e ro u s d if f r a c t io n p a tte r n s th ro u g h th e o p ­ t i c a l s y s te m in d ic a te d th a t th e b e s t m u lt ip le d if f r a c t io n p a tte r n s o c c u r r e d w h e n b o th th e lo n g itu d in a l a n d s h e a r s ta n d in g w a v e s w e re s im u lta n e o u s ly s tr o n g a n d n o r m a l to th e v ib r a t in g q u a r tz . In th e c a s e o f F ig . 4, th is c o n d itio n w a s e x c e e d in g ly w e ll f u lf ille d . I t is n o t ad ad >- CO ad LU o ad o < o z: o o LU CO LU LLi LINE AND MC. LU Q F IG .4. MULTIPLE DIFFRACTION SPECTRUM SHOWING POINT SPECTRA FROM THE SAME NEGATIVE. F : 10.0 ad CO o CO U-J 26 e a s y to f in d a fr e q u e n c y f o r w h ic h a p a r t ic u la r g la s s b lo c k th ic k n e s s i s so v e r y c lo s e ly id e n tic a l to an in t e g r a l m u lt ip le o f b o th lo n g itu d in a l a n d s h e a r w a v e le n g th s th a t s u c h a p e r fe c t p a tte r n c a n be o b s e rv e d . A s an e x a m p le o f a n o th e r ty p e o f m u lt ip le d if f r a c t io n p ic t u r e , F ig . 5 is in c lu d e d . T h e p r im a r y d if f r a c t io n o r d e r s o f th is p ic t u r e , ta k e n in th e s a m p le o f fu s e d s i li c a w it h u n p o la r iz e d lig h t a t an u l t r a ­ s o n ic fr e q u e n c y o f 11. 858 m e /s e c . a r e the S c h a e fe r -B e r g m a n n c i r c u l a r d if f r a c t io n p a tte r n and a s tr o n g lin e a r p o in t p a tte r n n o r m a l to th e s u r fa c e o f th e v ib r a t in g q u a r tz . o f th e f ig u r e . T h e s e a re in d ic a te d in P a r t B P a r t C o f th e f ig u r e i llu s t r a t e s th e a d d itio n a l c i r c u l a r p a tte r n s w h ic h a re due to m u lt ip le d if f r a c t io n . T h e f i r s t and s e c o n d o r d e r s o f th e lin e a r p o in t p a tte r n a c t as c e n te r s , o r c e n tr a l o r d e r s , f o r a d d itio n a l c i r c u l a r p a tte r n s , th e m u lt ip ly d if f r a c t e d p a tte r n s . a d d itio n tw o n e w lin e s o f p o in ts o c c u r . In T h e s p a c in g o f th e s e p o in ts v e r t i c a l l y is e q u a l to th e s p a c in g o f th e lo n g itu d in a l d if f r a c t io n p a tte r n , o r th e r a d iu s o f th e lo n g itu d in a l d if f r a c t io n c ir c le . H o r iz o n t a lly , h o w e v e r , th e s p a c in g is e q u a l to n e it h e r th e r a d iu s o f th e lo n g itu d in a l n o r o f th e s h e a r d if f r a c t io n c ir c le s . O ne n o te s th a t th e s e p o in ts l ie o n th e s h e a r d if f r a c t io n c i r c le s , a n d on c lo s e r e x a m in a tio n i t c a n be s e e n th a t th e y l ie on th e in t e r s e c t io n o f tw o s h e a r d if f r a c t io n c ir c le s . N o t e v e r y in t e r s e c t io n o f s h e a r c ir c le s p ro d u c e s a p o in t. F ro m ob­ s e r v a tio n and m e a s u r e m e n t o f a n u m b e r o f d if f e r e n t p h o to g ra p h s , s o m e s h o w in g a g o o d m a n y m o r e o f th e s e e x t r a p o in ts , it w a s fo u n d FIG. 5. A. PHOTOGRAPH OF MULTIPLE DIFFRACTION OF A SCHAEFER-BERGMANN CIRCULAR PATTERN TAKEN W IT H UNPOLARIZED LIGHT IN THE FUSED SILICA SAMPLE. B. APPROXIMATE SCALE DRAWING SHOWING THE PRIMARY ORDERS OF DIFFRACTION. C. DRAWING SHOWING HOW THE EXTRA CIRCLES DUE TO MULTIPLE DIFFRACTION HAVE AS THEIR CENTRAL ORDERS THE FIRST AND SECOND ORDERS OF THE LONGITUDINAL WAVE POINT DIFFRACTION PATTERN. th a t th e l o c i o f th e s e p o in ts a r e th e in t e r s e c t io n s o f a n y s h e a r w a v e d i f f r a c t i o n c i r c l e w it h one c e n te r e d a b o u t a lo n g itu d in a l d if f r a c t io n p o in t tw o o r d e r s a w a y in e it h e r d ir e c t io n . S c h a e fe r, B e rg m a n n , and G o e h lic h p o in t o u t th a t th e lig h t a p p e a rin g in th e s h e a r o r d e r s is e ll i p t i c a l l y p o la r iz e d and th a t th e se n se o f r o ta tio n o f a d ja c e n t o r d e r s is o p p o s ite . T h u s i t w o u ld be th a t lig h t a r r i v i n g at th e s a m e p o in t f r o m a lt e r n a te d if f r a c t io n o r d e r s w o u ld te n d to r e in f o r c e , w h ile l ig h t a r r i v i n g a t th e sa m e p o in t f r o m a d ja c e n t o r d e r s w o u ld te n d to c a n c e l. T h e fa c t th a t so m e o f th e s e p o in ts a p p e a r w h e re th e s h e a r w a v e c i r c le s no lo n g e r h a v e enough in t e n s ity to be s e e n m a y be due to e it h e r th is r e in f o r c e m e n t b y in v is ib le b u t p r e s e n t c ir c le s o f d i f f r a c ­ t io n o r b y d if f r a c t io n o f th e lig h t in th e fe w b r ig h t o r d e r s n e a r th e h o r iz o n t a l a x is o f th e p h o to g ra p h b y th e s tr o n g lo n g itu d in a l w ave w h ic h p ro d u c e d th e c e n t r a l v e r t i c a l lin e o f d if f r a c t e d p o in ts . In th is l a t t e r c a s e th e r e w o u ld in d e e d be m u lt ip le d if f r a c t io n a t th e in d ic a te d p o in t, e. g. , r e d if f r a c t i o n o f lig h t a p p e a rin g in o r d e r s w h o s e o r ig in w a s m u lt ip le d if f r a c t io n . 29 D e s c r ip t io n o f th e E x p e r im e n t a l A p p a r a tu s T h e O p tic a l S y s te m T h e a r r a n g e m e n t o f a p p a ra tu s on th e o p tic a l b e n c h is sh o w n s c h e m a t ic a lly in F ig . la m p . 6 . T h e lig h t s o u rc e w as a m e r c u r y a rc T h e lig h t f r o m th is la m p p a s s e d th r o u g h th e f i l t e r fo c u s e d o n th e s l i t S b y a s h o r t fo c a l le n g th le n s th e s l i t w a s c o llim a t e d b y th e le n s zer M P , th e g la s s b lo c k C L. F and w as T h e lig h t f r o m and p a s s e d th ro u g h th e p o l a r i ­ B , and th e a n a ly z e r A , to the le n s 'O . T h is le n s fo c u s e d th e im a g e o f th e s l i t on th e f i l m p la n e o f th e c a m e ra A n i r i s d ia p h r a g m I p la c e d ju s t b e fo r e the g la s s b lo c k l im i t e d the lig h t b e a m to k e e p lig h t f r o m p a s s in g a ro u n d th e b lo c k . s h u tte r K. ES w a s p la c e d b e tw e e n th e le n s O A n e le c t r ic and th e c a m e ra . Som e n o te s a b o u t th e s e o p t ic a l e le m e n ts : 1. T h e m e r c u r y a r c s e r v in g as a lig h t s o u rc e w a s f it t e d w it h th e f i l t e r F f o r e lim in a t in g a l l b u t th e X5461 g re e n lin e . It w as fo u n d to be fe a s ib le to re m o v e th e b lu e s e c tio n o f th is f i l t e r f o r m o s t p u rp o s e s . B y d o in g so th e in t e n s ity o f th e g re e n lin e w a s a p p r e c ia b ly in c r e a s e d , a llo w in g s h o r t e r e x p o s u re tim e s , w h ile the e ffe c t o f th e fa in t r e d lin e p a s s e d b y th e r e m a in d e r o f th e f i l t e r w a s n e g lig ib le . In s o m e c a s e s th e r e d lin e d id p ro d u c e a d if f r a c t e d f i r s t o r d e r , b u t it w a s w e a k , o u t o f fo c u s , and e a s ily ig n o re d . 2. T h e s l i t w a s a f u l ly a d ju s ta b le c o m m e r c ia l u n it w it h th e ja w s r e p la c e d b y r a z o r b la d e s . E a r ly a tte m p ts to a d ju s t the b la d e s to be cd n co JJJ “LU > W O < ”. O f li |— LU —! lli o ^ OQ J o i I < o < LU O ' ' CO ^ LU ^ CO I 5* v , LU GO CO E cc: I— LU C IVJ I GO ^ _J < q0 1 CO S CO < °q_ o —i ^( 0 I I I Gf I Q- »—I oo ® O CO U J ^ OF THE 2 COMPONENTS < CO LU o cc < >O LU CO ( a : I-. Z t UJ d l u □ ^ U Ico I co 31 p a r a l l e l w e r e f o r t u n a t e ly n o t e n t ir e ly s u c c e s s fu l, a n d as s o o n a s the c o n v e n ie n c e o f n o n - p a r a lle l ja w s w a s d is c o v e r e d , th e y w e r e a llo w e d to r e m a in a s th e y w e r e . D ue to th e c h a n g in g b r ig h tn e s s o f th e d if f r a c ­ t io n p a tte r n s f r o m b lo c k to b lo c k , th e t o ta l e x p o s u re tim e w a s d if f i c u lt to ju d g e . T h e c o n v e r g in g s l i t a llo w e d m o r e la titu d e in th is ju d g m e n t. D u r in g th e e a r ly a d ju s tm e n t o f th e s l i t a n ic k w a s a c c id e n ta lly p u t in th e b la d e s a t th e n a r r o w e r end. T h is n ic k , n e a r ly ro u n d in shape, w a s u s e d a s th e a p e r t u r e f o r th e p o in t s o u r c e p a tte r n o f e a ch d if f r a c ­ t io n p ic t u r e ; i t p r o v e d to be an im p o r ta n t p a r t o f th e o p tic a l a p p a ra tu s . 3. T h e p o la r iz e r and a n a ly z e r w e r e tw o - in c h d is k s o f H - P o la r o id m o u n te d in g la s s . C o m p le te e x tin c tio n w a s n o t p o s s ib le w it h th e s e e le m e n ts , w h ic h fa c t w a s h e lp fu l in th a t th e c r o s s e d p o la r iz e r - a n a ly z e r p o s it io n w h ic h p a s s e d th e m o s t lig h t w h e n v ie w in g th e w e a k s h e a r o r d e r s s t i l l a llo w e d ju s t enou g h o f th e s tr o n g lo n g i­ tu d in a l o r d e r s to p a s s to p h o to g ra p h the tw o s im u lta n e o u s ly . 4. c a m e ra . T h e f i l m s o r p la te s w e r e h e ld in a le n s le s s p la te - b a c k T h e s h u tte r w a s r e ta in e d f o r c o n v e n ie n c e in p r e p a r in g f o r a p h o to g ra p h . F o r p h o to g ra p h ic p la te s , s e v e r a l c u t - f i l m h o ld e r s w e r e m o d if ie d to h o ld tw o - in c h s q u a re s c u t f r o m E a s tm a n K o d a k 1 0 3 - F s p e c tr o s c o p ic p la te s . In g e n e r a l fa s t p h o to g ra p h ic e m u ls io n s w e r e u s e d to d e c re a s e e x p o s u re t im e , th u s le s s e n in g th e c h a n c e o f fre q u e n c y a n d te m p e r a tu r e d r i f t . 5 . T h e e le c t r ic a lly - o p e r a t e d s h u tte r w a s b u ilt b y th e a u th o r 32 to b e a s s im p le a m e c h a n is m as p o s s ib le . Its s o le p u rp o s e w a s to i n ­ t e r r u p t th e lig h t b e a m d u r in g th e p a r t o f th e e x p o s u re w h e n th e d r iv in g v o lta g e a p p lie d to th e q u a r tz w a s c u t o ff. I t c o n s is te d o f a tw o - in c h d is k o f lig h t - w e ig h t b la c k e n e d m e ta l m o u n te d on a t h in c o u n te rw e ig h te d r o d p iv o te d in th e m id d le . A 28 v o lt DC r e la y w a s a r r a n g e d to op en th e s h u t t e r w h e n v o lta g e w a s a p p lie d . cover a l l / 2 T h e s h u tte r d is k w a s a r r a n g e d to in c h h o le in th e a lu m in u m p la te on w h ic h i t w a s m o u n te d , a n d th e p la te w a s a tta c h e d to a h e a v y r o d to a llo w m o u n tin g on the o p t ic a l b e n c h in s u c h a w a y th a t th e h o le w a s c e n te re d on th e a x is o f th e o p t ic a l s y s te m . T h e E l e c t r i c a l S y s te m T h e e le c t r ic a l s y s te m c o n s is te d o f th r e e p a r ts , th e r a d io ­ fr e q u e n c y o s c il l a t o r w h ic h e x c ite d th e q u a r tz tr a n s d u c e r , the e x p o s u re t im in g c i r c u i t , and th e th e r m o - c o u p le c i r c u i t . th e o s c il l a t o r u n it is s h o w n in F ig . 7. v e r s io n o f a s h o r t- w a v e t r a n s m it t e r . T h e c i r c u i t d ia g r a m f o r T h e c i r c u i t i t s e l f is a m o d ifie d I t w a s c o n s tr u c te d b y th e a u th o r. I t c o n s is te d o f a v a r ia b le fr e q u e n c y o s c illa t o r , a b u ffe r - d o u b le r s ta g e , a n d a p o w e r a m p li f i e r . The o u tp u t o f th e a m p lif ie r w a s lin k - c o u p le d to a tu n e d ta n k c i r c u i t f o r m a tc h in g im p e d a n c e to th e h ig h im p e d a n c e q u a r tz . T h e v a r ia b le fr e q u e n c y o s c illa t o r a llo w e d c o n tin u o u s tu n in g o v e r s m a ll ra n g e s w h ile h u n tin g f o r d if f r a c t io n p a tte r n s , a n d it s c o n ­ t r o l w a s p la c e d in s u c h a p o s itio n as to be c o n v e n ie n t to th e o p e r a to r w h ile p e e r in g th r o u g h th e r e a r o f th e c a m e ra . A r a d io - fr e q u e n c y (if — I CVJ 0 >>Si ,y O N © © o S i -P 'r-Jr-H P © *H O Ph © © Ph £ uuuuuuuuu nn 03 • 3 ft +> to P 1 *H fj 3 0 ) h -H I 0 P3 © I 1 0 ,t4 © © X Si ft I O I 1 I I I fe c* A o? CO W D4 >> W u © © p U »© O © a K\ rH P H P •H O © O • •H © © •* Ph f t S © in OJ © © H t> o O P i 0 ©0 O I I m a 1 »“5t a 1 i i— l rH © i OJ H O p rH O a a n m n rn CVJ — n m r p iin p — \A A A A -'<+H**-1 fW C ir c u it o 03 © O s c illa to r r\u [ • • oj in t*- h U OJ OJ O - z f < o c t: lu < >- -J a : lu L u i— i— ^ oc: o tr _J X LU CO o 00 o 0 C o CD LU LU X 00 co LU cb n iX <> ot o> 8 I-C O o o < 36 e n e d r o o m w h e n e x p o s u re tim e s o f lo n g d u r a tio n w e re r e q u ir e d . T h e th e r m o c o u p le c i r c u i t c o n s is te d o f a fin e c o p p e r c o n s ta n ta n ju n c t io n s o ld e r e d to a 1 /4 in c h d ia m e te r d is k o f th in c o p ­ p e r , an ic e b a th , a n d a c o n tin u o u s ly o p e r a tin g , s e lf- b a la n c in g , r e c o r d in g p o te n tio m e te r . T h e e le c t r ic a l c o n n e c tio n s w e re c o n v e n tio n a l. The s m a ll c o p p e r d is k w a s p r e s s e d a g a in s t th e u p p e r s u rfa c e o f the g la s s b lo c k u n d e r a s m a ll p a d o f sponge r u b b e r b y m e a n s o f a f la t s p r in g . T h e th e r m o c o u p le c i r c u i t w a s n o t in te n d e d to g iv e a tr u e te m p e r a tu r e o f th e g la s s b lo c k , b u t o n ly to g iv e th e te m p e r a tu r e o f a p o r tio n o f th e s u r fa c e in o r d e r to p r e v e n t o v e r h e a tin g and in d ic a te w h e n a s te a d y s ta te h a d b e e n re a c h e d . n e a re s t 1 / 2 T e m p e r a tu r e re a d in g s w e r e ta k e n to th e d e g re e c e n tig r a d e . M o u n tin g o f th e G la s s B lo c k T h e g la s s b lo c k i t s e l f w a s m o u n te d on a s m a ll g la s s - c o v e r e d ta b le o n th e o p tic a l b e n c h . T h e m e th o d o f m o u n tin g th e q u a rtz c r y s t a l to th e b lo c k w a s as fo llo w s : A f t e r p o lis h in g a l l s u r fa c e s o f th e g la s s c u b e , i t w a s p la c e d u p ­ s id e d o w n on th e w o rk b e n c h . A s m a ll d o t o f s ilic o n e s to p c o c k g re a s e th e s iz e o f a m a tc h h e a d w a s p la c e d in th e c e n te r o f th e u p p e r s u r fa c e . T h e n a s t r i p o f a lu m in u m f o i l 1 1 /2 in c h e s w id e and 4 in c h e s lo n g w a s l i g h t l y p la c e d o v e r th e g re a s e s p o t. A p la te g la s s b lo c k one b y tw o b y tw o in c h e s , n o t o th e r w is e u s e d in th e in v e s tig a tio n , w a s p la c e d on th e a lu m in u m f o i l and p r e s s e d d o w n w it h as m u c h fo r c e as p o s s ib le to 37 s p r e a d th e g re a s e u n d e r th e f o i l in to a th in f i l m . T h is m e th o d g e n e r ­ a l l y e lim in a t e d a l l a i r b e tw e e n th e f o i l and th e g la s s s u r fa c e . h e a v y b lo c k w a s th e n re m o v e d . The T h e f o i l w a s fo ld e d d ow n on tw o s u r ­ fa c e s a d ja c e n t t a th e g re a s e d s u r fa c e so th a t one c o u ld h o ld th e b lo c k a n d f o i l as a u n it w ith o u t one s lip p in g w it h r e s p e c t to th e o th e r d u r in g th e n e x t s te p . A n e q u a l a m o u n t o f g re a s e w a s th e n p u t o n th e u p w a rd s u rfa c e o f th e f o i l on th e b lo c k . T h e q u a r tz c r y s t a l, one in c h s q u a re , w a s c le a n e d and p la c e d on th is d o t o f g re a s e . T h e p la te g la s s b lo c k w a s u s e d a g a in f o r p r e s s in g th e q u a r tz d ow n and c r e a tin g a n o th e r th in g re a s e la y e r w h ile th e b lo c k and f o i l on i t w e r e h e ld f i r m l y . W h e n as m u c h o f th e g re a s e h a d b e e n s q u e e z e d o u t as p o s s ib le , th e q u a r tz w a s c e n te r e d on th e g la s s b lo c k b y s lid in g i t w h ile s t i l l u n d e r p r e s s u r e . T h e h e a v y p ie c e o f p la te g la s s w a s la id a s id e . T h e a s s e m b ly o f q u a r tz , g la s s s a m p le , and a lu m in u m f o i l w a s in v e r te d and th e a lu m in u m f o i l t r im m e d so th a t one p ie c e a b o u t tw o in c h e s lo n g e x te n d e d f r o m one s id e . T h is p ie c e o f f o i l s e r v e d as th e u p p e r e le c tr o d e c o n n e c tio n on th e q u a r tz , w h ile th e t h in g re a s e la y e r s e r v e d as th e a c o u s tic a l c o n ­ d u c to r f r o m q u a r tz to g la s s . F o r s o m e g la s s s a m p le s w h ic h s e e m e d d i f f i c u l t to d r iv e a c o u s t ic a lly , a p la s t ic c e m e n t w a s u se d in p la c e o f th e g re a s e . T h e g la s s on th e s m a ll ta b le on th e o p tic a l b e n c h w a s c o v e re d w it h a p ie c e o f f la t a lu m in u m f o i l to s e r v e as the lo w e r q u a rtz 38 e le c tr o d e . M o u n tin g th e q u a r tz and b lo c k o n th e o p tic a l s y s te m s im ­ p ly c o n s is te d o f p la c in g th e m o n th e fo il- c o v e r e d ta b le and c o n n e c tin g th e e le c tr o d e s to the o s c il l a t o r w it h s m a ll b lip s . S in ce no g re a s e w a s u s e d u n d e r th e q u a r tz , th e th in f i l m o f a i r s e r v e d as a m is m a tc h o f a c o u s t ic a l im p e d a n c e , and l i t t l e e n e rg y w a s r a d ia te d d o w n w a rd . T h is m e th o d o f m o u n tin g a llo w e d one to change g la s s s a m p le s in th e s h o r t ­ e s t p o s s ib le t im e . 39 M e a s u re m e n t P ro c e d u re T h e p r o c e d u r e f o r ta k in g a m e a s u re m e n t p h o to g ra p h b e g a n w it h th e a d ju s tm e n t o f th e o p tic a l s y s te m . W ith th e g ro u n d g la s s v ie w in g p la te in th e c a m e r a an d a m a g n ify in g le n s fo c u s e d on th is p la te , th e c a m e r a w a s m o v e d u n t il th e s l i t im a g e w a s in s h a rp fo c u s . T h e n w ith th e r e m o v a l o f th e g ro u n d g la s s , th e s l i t im a g e w a s v ie w e d d ir e c t ly th r o u g h th e m a g n ify in g le n s . N e x t th e fre q u e n c y o f th e o s c illa t o r w as a d ju s te d u n t i l a d if f r a c t io n c o n fig u r a tio n w a s fo u n d w h ic h one w is h e d to r e c o r d . T h e t i m e r c i r c u i t w a s s ta r te d as w e ll as th e te m p e r a tu r e r e c o r d e r , a n d th e s y s te m w a s a llo w e d to r u n s e v e r a l m in u te s . A s m a ll b lo w e r p la c e d tw o fe e t o r so a b ove th e b lo c k w as tu r n e d on to k e e p th e a i r s t i r r e d up in th e v i c i n i t y o f th e g la s s b lo c k . A r i s e in te m p e r a t u r e w a s a lw a y s e x p e c te d due to d is s ip a tio n o f th e u lt r a s o n ic e n e r g y w it h in th e b lo c k in th e f o r m o f h e a t. A s th e te m p e r a tu r e c h a n g e d , th e fr e q u e n c y o f th e o s c il l a t o r h a d to be re a d ju s te d to ke e p th e d e s ir e d d if f r a c t io n p a tte r n . T h is w a s due to th e d e pe n d e nce on te m p e r a t u r e o f th e e la s t ic c o n s ta n ts and v o lu m e e x p a n s io n o f th e b lo c k w it h in c r e a s e o f te m p e r a t u r e w h ic h c a u s e d a s lig h t ch a ng e in th e s ta n d in g u lt r a s o n ic w a v e s y s te m w it h in th e b lo c k . I f th e te m p e r a tu r e k e p t in c r e a s in g , e it h e r th e c a m o p e r a tin g th e t i m e r w a s r e p la c e d w ith one w h ic h g a ve le s s q u a r tz e x c it a tio n tim e p e r m in u te , o r th e v o lta g e a p p lie d to th e r a d io - f r e q u e n c y p o w e r a m p lif ie r w a s lo w e r e d to re d u c e th e e n e rg y b e in g d is s ip a te d in th e g la s s . W h e n i t a p p e a re d th a t th e 40 s y s te m h a d s ta b iliz e d , th e r o o m w a s d a rk e n e d , th e p h o to p la te w a s p u t in p la c e , th e e le c t r ic s h u tte r w a s p o s itio n e d in th e o p tic a l s y s te m , th e t im in g c lo c k w a s r e s e t to z e r o , and th e e x p o s u re w a s begun. A m a r k w a s p u t on th e te m p e r a tu r e r e c o r d a t th e b e g in n in g and end o f th e e x p o s u re b y s h o r tin g th e th e rm o c o u p le le a d s m o m e n t a r ily w it h a ta p p in g k e y . D u r in g th e e x p o s u re th e fre q u e n c y m e te r w a s re a d s e v e r a l t im e s . F o r e a c h e x p o s u re th e fo llo w in g q u a n titie s w e re r e ­ c o r d e d in th e d a te r e c o r d b o o k : d a te , p h o to p la te n u m b e r, ty p e o f e m u ls io n , g la s s s a m p le n u m b e r, e x p o s u re t im e , s u rfa c e te m p e r a tu r e f r o m th e r e c o r d e r , R. F . q u a r tz c u r r e n t , R. F . a m p lif ie r p la te v o l t ­ a g e , p o la r iz e r - a n a ly z e r p o s itio n , t i m e r c a m ty p e , and fre q u e n c y . T h e le n g th o f a c tu a l e x p o s u re depe n d e d m a in ly on th e p h o to ­ g r a p h ic e m u ls io n s p e e d a n d th e b r ig h tn e s s o f th e d if f r a c t io n im a g e . T h e l a t t e r s o o n b e c a m e s o m e th in g th e o p e r a to r c o u ld ju d g e r e a d ily , and w it h th e c o n v e r g in g s l i t a w id e r la titu d e o f e r r o r in th is ju d g m e n t w a s a c c e p ta b le . D u r in g th e la s t s e v e r a l h u n d re d e x p o s u re s m a d e b y the a u th o r on E a s tm a n K o d a k 103 - F S p e c tr o g ra p h ic p la te s th e e x p o s u re tim e v a r ie d b e tw e e n 1 /2 to 1 m in u te . T h e a c tu a l t im e e la p s e d d u r in g th e e x p o s u re w a s g e n e r a lly o f th e o r d e r o f 3 to 10 m in u te s , h o w e v e r. C a lib r a t io n o f th e o p tic a l s y s te m w a s done w ith a c o m p a r is o n g r a tin g . T h is g r a tin g w a s o b ta in e d b y th e a u th o r b y p h o to g r a p h ic a lly r e d u c in g a la r g e d r a w in g o n to a g la s s p h o to g ra p h ic p la te . A n o p tic a l b e n c h a c c e s s o r y c o n s is tin g o f a c r o s s s lid e w h ic h h e ld tw o p o s ts w as 41 u s e d to h o ld th e c o m p a r is o n g r a tin g and th e g la s s b lo c k ta b le . Im m e d i­ a te ly a f t e r e a c h e x p o s u re f o r d a ta th e c a lib r a t io n g r a tin g w a s m o v e d in to th e p o s it io n f o r m e r l y o c c u p ie d b y th e g la s s s a m p le , th e p h o to ­ g r a p h ic p la te h o ld e r r a is e d in th e c a m e ra a b o u t 3 / 4 p o la r i z e r r o ta te d 9 0 ° , and an e x p o s u re o f a b o u t 6 o f an in c h , th e se co n d s m a d e . In t h is m a n n e r e v e r y u lt r a s o n ic d if f r a c t io n p a tte r n c o u ld be c o m p a re d w it h th e p a tte r n due to th e lin e g r a tin g . A c o m p a r a to r h a v in g a le a s t c o u n t o f 0. 001 m m . w a s u s e d f o r a l l l in e a r m e a s u r e m e n ts . In o r d e r to o b ta in th e g r a tin g c o n s ta n t f o r th e c o m p a r is o n g r a tin g , i t w a s m e a s u r e d o v e r a ra n g e o f 40 to 60 lin e s a b o u t 20 tim e s a n d an a v e ra g e v a lu e c a lc u la te d . F o r m e a s u re ­ m e n t o f th e d a ta r e c o r d e d on th e p h o to g ra p h ic p la te s , a s e ttin g w a s m a d e a n d r e a d on e a c h lin e te n tim e s . T h e fr e q u e n c y o f th e v o lta g e a p p lie d to th e p ie z o - e le c t r ic q u a r tz w a s m e a s u r e d to th e n e a r e s t k ilo c y c le p e r s e c o n d on a r e lia b le f r e ­ q u en cy m e te r. T h is m e t e r w a s c h e c k e d a g a in s t r a d io s ta tio n W W V a n d fo u n d to h a v e a d e v ia tio n m u c h le s s th a n one k ilo c y c le p e r se co n d . T h e m a x im u m e r r o r in d e te r m in in g th e fr e q u e n c y w a s e s tim a te d to be le s s th a n one k ilo c y c le p e r s e c o n d on a l l r e a d in g s . T h e d e n s ity o f th e g la s s s a m p le s w a s d e te r m in e d to fiv e s i g n i f i ­ c a n t f ig u r e s b y w e ig h in g th e b lo c k s in w a te r and in a i r on an a n a ly tic a l b a la n c e , ta k in g e v e r y p r e c a u tio n . tw ic e w it h g o o d a g re e m e n t. T h e s e m e a s u r e m e n ts w e re re p e a te d 42 E x p e r im e n t a l M a t e r ia ls and R e s u lts T h e v e lo c it ie s a n d d e n s itie s o f th ir t e e n d if f e r e n t ty p e s o f o p t i­ c a l g la s s w e r e m e a s u r e d b y th e m e th o d s g iv e n in th is p a p e r. N in e s a m p le s o f B a u s c h a n d L o m b o p tic a l g la s s w e re c h o s e n fro m c a ta lo g to c o v e r th e ra n g e f r o m the lig h t e s t to th e dense ty p e s . m o a t t h e ir O n e in c h c u b e s w e r e c u t, a n n e a le d , and p o lis h e d f o r us b y th a t c o m ­ pany. T h r e e s a m p le s o f r a r e e a r th o p tic a l g la s s w e re o b ta in e d f r o m th e E a s tm a n K o d a k C o m p a n y . th a n one in c h c u b e s . T h e s e s a m p le s w e r e s lig h t ly s m a lle r T h e fu s e d s i li c a s a m p le w as o b ta in e d f o r us b y th e O w e n s - I llin o is G la s s C o m p a n y . I t w a s u n d e rs to o d th a t th is s a m p le w a s o f th e h ig h e s t q u a lity in r e s p e c t to it s h o m o g e n e ity . T a b le s A and B g iv e th e p e rc e n ta g e c o m p o s itio n b y w e ig h t o f th e s e s a m p le s as g iv e n b y th e r e s p e c tiv e g la s s m a n u fa c tu r e r . a s s u m e d to be 1 0 0 % s ilic o n d io x id e . T h e fu s e d s i li c a s a m p le w a s S a m p le s Glass CVJ CVJ Per Cent C o m p o s itio n by W e ig h t, D is p e r s io n , and Index of R e fra c tio n of Bausch and Lomb ^ o I CO fa O 0 °? fa o I tr- o ^ ffl °? Q o in CO * rH ■ rH in i i CO O . 1 OJ I CO -sH CD I rH I • O CO I • O I CVJ o in i> 43 00 • CO N ( l> Tjl lO H CO N . . I r— I CVJ i ^ in o* in o o ^ 1 it-’ CVJ tH CO OJ in J> t i> pq ® Q o O CO O CVJ CO rH co I I I . o’ I I I o in co cvi co i> "**< co CO in co* co cCO • . 1 . 1 co CO 1 CD 1 CO co CM CM I CO O *> PQ °? H o t> ^1 23!1 fr. CO fa1 o1 r—l ^ s f t1 05 i O o co CO i> I o ^ o i «o r\ lO 8 ? m © 1 1 1 1 o CD CD CO o' CO rH CO lO 05 J> O I CO i co o o m th i CO CO CM CVJ I in co co t - i i CD r— I cm m co tr­ io in i 00 CM O O tr-" T-I (M* OJ* LO CM I . . I o o in I (N I I 1 I o CJ CO CD rH in co’ in CO CM LO c3 rH in C- o ErH* cm CO I . . . I OJ rH rH 00 rH m • • . i o CM tr- i J> r—1 CO © CO 1 . . I I I 1 1 rH CO 1 f 1 1 o CD I rH 00* in LO . rH m . CO CO Q £ 0 Or Fh O CQ Jzj M s ^0 J3 o s rH CD o g Qa JctJcvin Q O Q FQi ^ c SraCM fa " bC% vjctjjO in f a £ f a p Q O C Q S ! iS i< J in < ! g o s .s .5 i iO -H » S5 Q a 0 44 o ID I w w £ tb •-P-J o co 00 CM o O CM CM CO 03 OJ (U A o oo CO I w w CM o CM CO 00 PQ H t-3 I CM CO CM o W 03 CQ 0 ) n •r-l X o ♦1 o> ou a JH 02 02 cd rH O •H H m !>"> CO oCM oCM O cd cd A J H PQ CO o 0 m PQ CM LO Xfl + oCM O cd cd H PQ co § < 45 D i f f r a c t i o n p a tte r n s w e re o b ta in e d f r o m e a ch o f th e s a m p le s as f a r a s p o s s ib le a t fr e q u e n c ie s o f 1 0 , 1 0 . 5 , 1 2 , 13. m e g a c y c le s p e r s e c o n d , u s in g X - c u t q u a rtz p la te s , 5 , 14, 15, a n d 16. 1 5 in c h s q u a re , o f fu n d a m e n ta l fr e q u e n c ie s 1. 5, 2, 3, 4, and 5 m e g a c y c le s p e r se co n d . T h e s e p a tte r n s w e r e m e a s u r e d w it h a r e lia b le c o m p a r a to r , a lo n g w ith th e 3 o r 4 o r d e r d if f r a c t io n p a tte r n p ro d u c e d b y th e c o m p a r is o n g r a t ­ in g on th e s a m e g la s s p la te . s ta n t (d = K n o w in g th e c o m p a r is o n g r a tin g c o n ­ 0. 2319 m m . + 0 . 04%), th e w a v e le n g th s w e re c a lc u la te d b y u s in g e q u a tio n s (7 a ) a n d (7 b ). T h e v e lo c it ie s w e re c a lc u la te d f r o m th e v a lu e s o f th e fr e q u e n c y and th e w a v e le n g th s u s in g e q u a tio n s ( 8 a) a n d ( 8 b ). T a b le C is a s a m p le ta b u la tio n o f a l l th e v e lo c it y m e a s u r e ­ m e n ts f o r a p a r t i c u l a r s a m p le o f g la s s , in th is c a s e th e B a u s c h and L o m b ty p e D B F - 1 . fro m g la s s . 1 0 to 16. 5 T h e fr e q u e n c y c o lu m n s h o w s th a t a f u l l s p re a d m e g a c y c le s p e r s e c o n d w a s p o s s ib le f o r t h is ty p e o f In c e r t a in o f th e s a m p le s , n o ta b ly th e E a s tm a n K o d a k g la s s e s , i t w a s n o t p o s s ib le to fin d s u ita b le d if f r a c t io n p a tte r n s a t s o m e o f th e h ig h e r fr e q u e n c ie s . T h e te m p e r a tu r e s in th e n e x t c o lu m n w e r e th o s e a t a p o in t on th e u p p e r s u r fa c e o f th e s a m p le a n d, a s s a id b e fo r e , w e r e n o t t r u l y in d ic a tiv e o f th e in t e r n a l te m p e r a tu r e o f th e g la s s s a m p le d u r in g it s p e r io d o f e x c ita tio n . p o s e s o n ly . n o te d . T h e y a re f o r c o m p a r is o n p u r ­ N o tr e n d o f ch a ng e o f v e lo c ity w it h th is te m p e r a tu r e w a s 48 TABLE C S a m p le T a b u la tio n o f a l l M e a s u re m e n ts on th e S a m p le o f B a u s c h and L o m b T y p e D B F - 1 G la s s T r ia l F re q u e n c y m e /s e c T e m p e r a tu r e oc ; •- L o n g itu d in a l Shear O rd e rs m /s e c m /s e c 2589. 1 11. 749 26. 5 2 1 1 .8 1 5 26. 5 4361. 3 1 0 . 0 2 1 27. 4370. 4 1 3 .9 8 0 29. 5 1 4 .0 4 2 29. 4 367. 6 1 4 .7 3 1 28. 4366. 7 1 6 .6 0 5 25. 5 4369. 2 8 13. 532 29. 43 62 . 2 9 1 0 .5 3 5 25. 5 4358. 1 0 13. 534 27. 5 43 66 . 1 1 1 3 .4 6 5 28. M e a n V e lo c it ie s P ro b a b le N u m e r ic a l E r r o r P r o b a b le E r r o r (%) 4 2585. 4 2589. 8 2590. 2597. 4 6 2591. 4365. 2590. 3 3 . 07% 4 . 1 0 % 47 T h e n e x t tw o c o lu m n s a re th e u lt r a s o n ic v e lo c it ie s as c a lc u ­ la t e d f r o m th e m e a s u r e m e n ts o f th e d if f r a c t io n p a tte r n s . The n um ber o f o r d e r s o f th e lo n g itu d in a l w a v e d if f r a c t io n p a tte r n f o r th e p a r t ic u ­ l a r p h o to g ra p h is g iv e n i n th e la s t c o lu m n . T h e s h e a r w a ve p a tte r n s h a d , o f c o u r s e , o n ly f i r s t o r d e r p a tte r n s . N o te th a t it is o n ly o c c a s ­ io n a lly th a t one g e ts a u s e fu l d if f r a c t io n p a tte r n r e s u lt in g fr o m b o th th e lo n g itu d in a l and s h e a r w a v e s . T h e p a tte r n s w h e re s im u lta n e o u s d if f r a c t io n due to b o th w a v e s o c c u r r e d o fte n sh o w e d m u lt ip le d if f r a c t io n . T h e m e a n v a lu e s o f th e v e lo c it ie s a re sh o w n u n d e rn e a th th e v e lo c it y c o lu m n s . T h e n u m e r ic a l and p e rc e n ta g e p r o b a b le e r r o r s a re g iv e n n e x t b e lo w . A m o n g a l l th e s a m p le s th e m a x im u m p ro b a b le p e r c e n t e r r o r s w e r e 0. 13% f o r th e lo n g itu d in a l v e lo c it ie s and 0. 25% f o r th e s h e a r v e lo c it ie s . 0 .1 7 % . A v e r a g e s v a lu e s w e r e r e s p e c t iv e ly 0 . 1 0 % and A w e ig h te d m e a n o f th e lo n g itu d in a l v e lo c it ie s o f e a ch o f th e s a m p le s , w e ig h t b e in g a s s ig n e d to e a c h m e a s u r e m e n t a c c o r d in g to th e n u m b e r o f o r d e r s m e a s u r e d , w a s c o n s id e r e d , b u t in g e n e r a l th e ch a ng e o f th e v a lu e o f th e m e a n w a s le s s th a n th e p ro b a b le n u m e r ic a l e rro r. T h e r e s u lt s o f th e m e a s u r e m e n ts o f th e v e lo c it ie s and d e n s i­ t ie s o f a l l th e g la s s s a m p le s a re lis t e d in T a b le D . T h e p ro b a b le e r r o r c la im e d f o r t h is s e t o f m e a s u re m e n ts is th e m a x im u m v a lu e n o te d in th e la s t p a r a g r a p h , 0. 13%, f o r lo n g itu d in a l v e lo c it ie s and 48 TABLE D V e lo c it ie s a n d D e n s itie s o f th e G la s s S a m p le s G la s s Type L o n g itu d in a l V e lo c it y (m /s e c ) S hear V e lo c it y ( m /s e c ) B S C -1 5893. 3572. 2 .4 7 6 6 C -l 5797. 3473. 2 .5 2 6 8 C F -1 5086. 3088. 2 .6 9 2 4 L F -1 4597. 2762. 3. 1742 L B C -2 5333. 3109. 3. 1424 D B F -1 4365. 2590. 3 .6 0 0 8 D F -2 5156. 2908. 3 .6 4 4 1 E D F -4 3704. 2185. 4 .7 1 8 9 D B C -2 4140. 2469. 3. 7813 E K -1 1 0 5679. 3102. 4 .1 3 1 7 E K -3 3 0 5578. 3039 4 .5 7 2 0 E K -4 5 0 5804. 3143. 4 .6 2 9 3 Fused S ilic a 5963. 3766. 2 .2 0 2 7 D e n s ity ( g /c c ) 49 0. 25% f o r s h e a r v e lo c it ie s . s it ie s w a s le s s th a n 0 T h e e r r o r in the m e a s u re m e n t o f th e d e n ­ . 05%. T h e e la s t ic m o d u li o f th e s a m p le s a re g iv e n in T a b le E , as c a lc u la te d f r o m th e v a lu e s in T a b le D and e q u a tio n s (9 ) to (1 3 ). C a lc u 18 la te d w it h th e m a th e m a tic s o f p ro p a g a tio n o f p r e c is io n in d ic e s , the p r o b a b le e r r o r s in p * , A , and k a n d E r e s p e c t iv e ly a re 0. 7% and 0. 8 a re 0 . 5%, w h ile th o s e o f