ALIGNMENT CHART FOR CALCULATION OF REFRACTIVE INDEX FROM THE DEVIATION OF LIGHT BY A PRISM HonacB WrNcuntl, Yale Uniaersity, New Haaen, Conm.

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1 ALGNMENT CHART FOR CALCULATON OF REFRACTVE NDEX FROM THE DEVATON OF LGHT BY A PRSM HcB WrNcutl, Yle Uierity, New He, Cm. Arcr A ligmet chrt i preeted by me f which the refrctive idex f prim i btied frm the gle f deviti f iight pig thrugh it, d the prim gle' New iteret i the prim methd fr meuremet f refrctive idice h reulted frm the develpmet f ew deig fr gimeter (Wlfe d Frkli,1949 Wlfe, 1948). Such iteret ugget tht the prim methd d cmputti therefr might prfitbly receive dditil tudy. Thi te decribe imprved mgrm fr the cmputti. Smith (1906) decribed chrt fr ue with the miimum deviti methd, ccurte t the eret.005. Other reducti f equti (1) r (2) t chrt frm re t kw t the writer. Equti (1) d (2) re ued fr cmputig the refrctive idex, z, frm meuremet f the prim gle,, d the deviti, d, f light bem pig thrugh it. i ( * d) SN 4 (1). (-ld) S -- 2 & l - 2 (2) t i bviu tht y mgrm fr e wiil l give luti f the ther, prvided iy tht the cle fr d d, hve tw et f umericl clibrti difierig by fctr f tw. Equti (1) i the frm ued whe the light eter (r leve) e ide f the prim t rml icidece (Frd, 1932, p.240); equti (Z) i the frm ued whe the deviti f light i miimum (Frd, 1932,p.242). Thee equti my be lved by me f the ligmet chrt reprduced i Fig. 1. A tright lie pig thrugh the cle d d. t pit crrepdig repectively t the prim gle d t the gle f deviti will p thrugh the z-cle t pit crrepdig t the refrctive idex f the prim. t i t be ted tht the ier clibrti f the -, d d-cle pply t the ce f rml icidece f the light ry up e prim fce, d the uter (lt-lettered) clibrti, t the ce f miimum deviti. The crdite f the vriu pit lg ech cle hve bee btied fr pprximtely twice my pit re reprduced here, 287

288 HORACE WNCHELL d whe pltted chrt meurig 100 cm. by 80 cm., redig f refrctive idex c eily be btied tht re ccurte t the eret 0.003, r better, frm gulr dt ccurte t the eret miute f rc.

2 288 HORACE WNCHELL d whe pltted chrt meurig 100 cm. by 80 cm., redig f refrctive idex c eily be btied tht re ccurte t the eret 0.003, r better, frm gulr dt ccurte t the eret miute f rc. Drverrw l rhe Ar-rcuBNr Cer Equti (1) c be rewritte fllw: i - i c d - c i d : 0 (3) determit frm, thi i: O1 c i 0 cd -id :0 Rerrgemet f the determit give the fllwig tdrd frm (Mckey, 1944,. 85): 0 t 1 l/01 ecd -td Equti (4) i recgized the equti f tright lie thrugh the three pit, rcl:o, yr:t ; r2--lf, yz:o; rrd x:ec d, y: -t d'. t will be ted tht the firt pit i determied lely by the prim the ecd by the refrctive idex rz, d the third by the gle f deviti d. The firt lie lg the pitive y-xi, the ecd, lg the pitive r-xi; the third, lg curve i the qudrt f pitive r, egtive y (Fig.2A). 30 :0 (4) Frc.2 xi The gle betwee the r- d the y-xi de t hve t be 90'. The vlue 30" wuld give tifctry chrt which i ketched ifig.28. T fcilitte plttig the d-cle rdiry grph pper, the rectgulr crdite (rt', yt') f the cle pit my be fud fter the bve chice f 30 fr the gle betwee the *-, d the 1-xi i ettled (equti

3 (f r >< { (rl \.Q t\) N) (.r1 (,1 ul Ol 1,,,,t.,,,t,.,,r,.,,t,,,.1,,,,t,,,,r,,,,r,,,,r,,.,r,,,,r,,,,t,,,,t,,,,t,,,,1,,,,t,,,,t,,,,,,.,r,'''L'''L $ ' PRSM ANGLE - Mefhd f Nrml cidece O llelhd l lliimu Devili.tu C).4) -.3,rE," le i.i.[ii $d. OQ % c/r e+ 3.F,lg. z :16 -lg frl z m -Tt f { Tl O e ge ' t.tl r.tl - f.z. Ec) rrl T1 C) J TJ. qm DEVATON d - llethd f frliimum Oevili d Methd f Nrmf tcidece (, g)

4 ALGNMENT CHART FOR CALCULATNG REFRACTVE NDEX 289 5), r the rigil crdite (r3,y3), meured, prltrel trhe *e r theew glej 30"' my be ued uggeted i the figure. N cmputig whtever i ecery fr the cle f d ; the * d y3 vlue fr the cle f d' my likewie be fud i y tble f tget d ect, but the mre cveiet rectgulr crdite r,1t d ytmut be cmputed. A prjective trfrmti f equti (4) (Mckey,1944, p. 97) prduce mre ueful chrt, d t the me time give it better hpe with elected pit f the -, d d-cle t the crer f qure r rectgle. Thi trfrmti i ccmplihed by multiplyig bth ide f equti (+) by determit (6) i which the ', b,, d c, re ctt t be evluted. The prduct i give fllw: re' : i 30' ec d t r' : c 30" ec d - t d,\ rhcl 2 bz c2 3hc t0 () (6) btt1,ct bt c A1 t cr c bzt* cz bt ct A2 -f ez A3 t lecd. - htd, ct zecil - bzecd, cz ^*d - btt""d+ r d ecd - b eci+z' 1 :0 (7) We my che t mke the ligmet chrt meter qure, with the -cle lg the left edge rgig frm 20 t 45", d the d-cle curvig iwrd frm the right edge d rgig frm 10't 45". ice clculti re implified by tkig trre rge f the -cle t 45', thi qure hpe w elected, thugh the upper fifth { the qure i mitted i Fig. 1. Plcig the rigi f crdite t the lwer left crer, we bti the fllwig eight equti: Origi: (*1:0, 1t:g; bt t 20 * ct.tt:----:0 ' b:t20 -c, Upper left crer (*1: Q, lr: 1.00 meter) : ht45 * ct #1 - :----:0 bt45 * cz Upper right crer f3:1, y:1) -- trr ec 10-6r t 10 * cr d3s c10-drt10*er Lwer right crer (r3: 1, y3: 0) rec45-6t45*ct 3 ec 45 - b t 45 * c _1 - r b, t20 c, /r: :0 bt t 20! et bz t cz -1 bt t 45 * ct ec 10 - bztl0 * cz ec 10 - htl0 ct ec45-bzt45 lcz :0 ec45 - ht(s c Thee eight equti cti ie ukw qutitie f which e (8)

$The fil luti give the elemet f the multiplyig determit (6) fllw: r : 0.325911 br : 0 c\: e : 0.126998 bz : 0 '753776 c, : -0 '273521, : -0.$

5 290 HORACE WNCHELL (c) i rbitrrily put equl t uity, reducig the ytem t eight equiir6 i eight ukw. pecti hw thtfu: cr:0, implifyig the ytem t"ce. The fil luti give the elemet f the multiplyig determit (6) fllw: r : br : 0 c\: e : bz : 0 ' c, : -0 '273521, : bt: -0' cz: J Thee vlue re ubtituted it equti (7) fr the ctructi f the fil ligmet chrt, which i reprduced i Fig' 1' The tw equti fr the -cle re kw t led t tright cle, d c therefre be cmbied it igle equti f ditce r2l (Fig' 3) lg the lie frm it pit f iterecti with the y-xi t y: -0'27435' A hw by the dhed lie i Fig. 3, the upper fifth f the qure i mitted. The fiihed chrt i preeted Fig. 1. (e)!]j4]l F TLN.FHED CHART Frc. 3 RrrruNcr F, W. E. (1932), D' Textbk f Mierlgy. New Yrk (Jh!\riley d S). Mcrv, C. D. (1944), Grphicl Sluti' New Yrk (Jh Wiley d S)' urrrr, G. F. Hr (1906), O the methd f miimum deviti fr the determiti f refrctive idice: Mierl. Mg.,14, 191 ( )' Wtr, C. W. (1948), A ew tw-circle gimeter: Am' Mierl',33' 739' Wr-lr;, C. W., ln FeNxr.rN, Vrctwr (1949), Refrctive idice by the prim methd the tw-circle gimeter: Am. Mierl",34t 893' Mucript receitted N' 6, 1950-

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