
jyaamitiya prakashiki

jyaamitiya prakashiki, yaa kiran prakashiki, prakashiki kaa ack model haye joe "kiranon" key sandarbh mein prakaash prasaar kaa varnan kartaa haye. jyaamitiya prakashiki mein kiran ack amoort haye joe una raaston key anuman key liye upayogi haye jinake saath prakaash kuchh paristhitiyon mein failata haye.
jyaamitiya prakashiki kii saral dhaaranaon mein prakaash kiranen shamil hainh
jyaamitiya prakashiki kuchh optical prabhaavon jaise vivartan aur hastakshep key liye jimmedaar naheen haye. yeh saralikaran vyavhaar mein upayogi haye; yeh ack utkrisht anuman haye jaba tarang dairdhya sanrachanaon key aakar kii tulanaa mein chhota hotaa haye jisake saath prakaash paraspar kriya kartaa haye. takneeken vishesh roop seey imaging key jyaamitiya pahaluon kaa varnan karane mein upayogi hain, jisamen optical vichalan bhee shamil hain.
spashteekaran.
ack prakaash kiran ack rekha yaa vakr haye joe prakaash key tarang-agra key lambavat haye (aur isaliye tarang sadish key saath sanrekhiya haye).
ack prakaash kiran kii thodi adhik kathor paribhasha firmate key siddhant seey milati haye, joe bataata haye kii prakaash kii kiran dwara dou binduon key beach liya gayaa maarg vaha maarg haye jise cumm seey cumm samay mein paar kiya jaa sakata haye.
jyaamitiya prakashiki koo aksar paraakshiya sanniktan, yaa "chhote konn sanniktan" banaakar saral banaaya jaataa haye. ganitiya vyavhaar taba raikhik hoe jaataa haye, jisase optical ghatakon aur pranaliyon koo saral matricks dwara varnit kiya jaa sakata haye. yeh gausi prakashiki aur "paraxial ray tracing" kii takneekon kii or leey jaataa haye, jinka upayog optical system key buniyaadi gunon koo khojane key liye kiya jaataa haye, jaise kii anumaanit chhavi aur vastu kii sthiti aur aavardhan.
pratibimb.
darpan jaisi chamakdaar satahen prakaash koo saral, anumaanit tareeke seey pratibimbit karati hain. yeh pratibimbit chhaviyon key utpaadan kii anumati detaa haye joe antariksh mein ack vaastavik (vaastavik) yaa bahishkrit (aabhaasi) sthaan key saath judey hoe sakate hain.
aisee satahon key saath, paraavartit kiran kii disha usa konn seey nirdhaarit kii jaati haye joe aapatit kiran satah key saath samanya banaati haye, usa bindu parr satah key lambavat rekha jahaan kiran takaraati haye. ghatana aur paraavartit kiranen ack hii tala mein hoti hain, aur paraavartit kiran aur satah key beach kaa konn samanya ghatana kiran aur samanya key beach key konn key samaan hotaa haye. ise pratibimb key niyam key roop mein jaanaa jaataa haye.
sapaat darpanon key liye, pratibimb key niyam kaa tatparya haye kii vastuon kii chhaviyaan seedhi hoti hain aur darpan key peechhe utani hii doori hoti haye jitani vastuon kii darpan key saamane hoti haye. chhavi kaa aakar vastu key aakar key samaan haye. (ack sapaat darpan kaa aavardhan ack key barabar hotaa haye.) kaanoon kaa yeh bhee tatparya haye kii darpan chhaviyaan samaan roop seey ulte hotey hain, jise baaen-daaen vyutkram key roop mein maanaa jaataa haye.
ghumaavdaar satahon vaale darpanon koo kiran anurekhan aur satah parr pratyek bindu parr pratibimb key niyam kaa upayog karke model kiya jaa sakata haye. paravalayik satahon key saath darpanon key liye, darpan parr samanantar kiranon kii ghatana paraavartit kiranon kaa utpaadan karati haye joe ack samanya phocus parr abhisaran karati hain. anya ghumaavdaar satahen bhee prakaash koo kendrit curr sakati hain, lekin vichalan key kaaran vichalan key kaaran dhyaan koo antariksh mein dhabba lagaaya jaa sakata haye. vishesh roop seey, golakar darpan golakar vichalan pradarshit karate hain. ghumaavdaar darpan ack seey adhik yaa cumm aavardhan key saath chhaviyaan banaa sakate hain, aur chhavi seedhi yaa ulta hoe sakati haye. darpan mein pratibimb dwara banaai gaee ack seedhi chhavi hamesha aabhaasi hoti haye, jabaki ack ulta chhavi vaastavik hoti haye aur ise screen parr prakshepit kiya jaa sakata haye.
apavartan.
apavartan taba hotaa haye jaba prakaash antariksh key usa kshetra seey gujarta haye jisamen apavartan kaa soochkaank badalata haye. apavartan kaa sabse saral mamla taba hotaa haye jaba apavartan sootra _ 1 key soochkaank key saath ack samaan madhyam aur apavartan sootra _ 2 key soochkaank key saath ack anya madhyam key beach ack interfaces hotaa haye. aisee sthitiyon mein, snell kaa niyam prakaash kiran key parinami vikshepan kaa varnan kartaa haih
jahan sootra _ 4 aur sootra _ 5 kramshah samanya (interfaces key liye) aur ghatana aur apavartit tarangon key beach key konn hain. yeh ghatana prakaash kii badalati gati seey bhee judee hui haye jaisa kii oopar diye gaye apavartan soochkaank kii paribhasha seey dekhaa gayaa haye jiska tatparya haih
jahan sootra _ 7 aur sootra _ 8 sambandhit madhyam key madhyam seey tarang wegg hain.
snell key niyam key vibhinn parinamon mein yeh tathya shamil haye kii uchch apavartan soochkaank vaali samagri seey apavartan key cumm soochkaank vaali samagri mein yatra karane vaali prakaash kiranon key liye, interfaces key saath baatchit key parinamswarup shoonya sancharan sambhav haye. iss ghatana koo kull aantarik pratibimb kahaa jaataa haye aur yeh fiber optics praudyogiki kii anumati detaa haye. jaise hii prakaash sanket ack fiber optic cable key neeche yatra karate hain, way kull aantarik pratibimb seey gujarate hain jisase anivarya roop seey cable kii lambai parr koee prakaash naheen khou jaataa haye. paraavartan aur apavartan key sanyojan kaa upayog karke dhruvikrit prakaash kiranon kaa utpaadan karna bhee sambhav haih jaba ack apavartit kiran aur paraavartit kiran ack samkon banaate hain, tou paraavartit kiran mein "samtal dhruvikaran" kaa guna hotaa haye. iss tarah key paridrishya key liye aavashyak ghatana konn koo sharaab banaane vaale key konn key roop mein jaanaa jaataa haye.
snell key niyam kaa upayog prakaash kiranon key vikshepan kii bhavishyavani karane key liye kiya jaa sakata haye kyonki way "raikhik media" seey gujarate hain jaba taka kii apavartan key soochkaank aur media kii jyaamiti gyaat hain. udaaharan key liye, ack prism key madhyam seey prakaash key prasaar key parinamswarup prakaash kiran prism key aakar aur abhivinyas key aadhar parr vikshepit hoe jaati haye. isake alawa, choonki prakaash kii vibhinn aavrittiyon mein adhikansh samagriyon mein apavartan key soochkaank thode alag hotey hain, isaliye apavartan kaa upayog failaav spectra kaa utpaadan karane key liye kiya jaa sakata haye joe indradhanush key roop mein dikhaai detaa haye. prism key madhyam seey prakaash koo paarit karate samay iss ghatana kii khoj kaa shreya prasiddh roop seey isaik neuton koo diyaa jaataa haye.
kuchh madhyamon mein apavartan kaa soochkaank hotaa haye joe sthiti key saath dheere-dheere badalata haye aur iss prakaar, prakaash kiranen seedhi rekhaaon mein yatra karane key bajaay madhyam key madhyam seey vakr hoti hain. yeh prabhaav germ dinon mein dekhe jaane vaale chamatkaron key liye jimmedaar haye, jahaan havaa key apavartan key badalate soochkaank key kaaran prakaash kiranen jhukati hain aur doori mein (jaise kii paani key pool kii satah parr) specular reflection kii upasthiti paida karati hain. jiss samagri mein apavartan kaa ack alag soochkaank hotaa haye, usey gradient-index (grin) samagri kahaa jaataa haye aur isamen photocopier aur scanner sahit aadhunik optical scanning praudyogikiyon mein upayog kiye jaane vaale kaee upayogi guna hotey hain. iss ghatana kaa adhyayan pravanata-soochkaank prakashiki key kshetra mein kiya jaataa haye.
ack upkaran joe apavartan key kaaran parivartit yaa vichalit prakaash kiranon kaa utpaadan kartaa haye, usey lens key roop mein jaanaa jaataa haye. patale lens donon taraf fokal point paida karate hain jinhen lensmaker key sameekaran kaa upayog karke model kiya jaa sakata haye. samanya taur parr, dou prakaar key lens maujood hainh uttal lens, joe samanantar prakaash kiranon koo abhisaran kaa kaaran banate hain, aur avtal lens, joe samanantar prakaash kiranon koo vichalan kaa kaaran banate hain. inn lenson dwara chhaviyon kaa utpaadan kaise kiya jaataa haye, isaki vistrit bhavishyavani vakr darpanon key samaan kiran-anurekhan kaa upayog karke kii jaa sakati haye. isi tarah ghumaavdaar darpanon key liye, patale lens ack saral sameekaran kaa paalan karate hain joe ack vishesh fokal lambai (sootra _ 9) aur vastu doori (sootra _ 10) dee gaee chhaviyon key sthaan koo nirdhaarit kartaa haih
jahan sootra _ 12 chhavi key saath judee doori haye aur ise parampara dwara nakaratmak maanaa jaataa haye yadi lens key usee taraf vastu key roop mein aur sakaratmak yadi lens key vipareet taraf haye. avtal lens key liye fokal lambai f koo nakaratmak maanaa jaataa haye.
aaney vaali samanantar kiranen ack uttal lens dwara ack ulte vaastavik chhavi mein kendrit hoti hain, joe lens seey ack kendra kii lambai parr, lens key door kii or hoti hain. 
seemit doori parr kissy vastu kii kiranen kendra kii doori kii tulanaa mein lens seey aage kendrit hoti hain; vastu lens key jitani karib hoti haye, chhavi lens seey utani hii aage hoti haye. avtal lens key saath, aaney vaali samanantar kiranen lens key madhyam seey jaane key baad iss tarah seey alag hoe jaati hain kii way lens seey ack fokal lambai kii ack seedhi aabhaasi chhavi parr utpann hoti hain, lens key usee taraf jiss parr samanantar kiranen aaa rahee hain. 
seemit doori parr ack vastu seey kiranen ack aabhaasi chhavi key saath judee hoti hain joe kendra kii lambai kii tulanaa mein lens key karib hoti hain, aur lens key usee taraf hoti hain joe vastu key roop mein hoti hain. vastu lens key jitani karib hogi, aabhaasi chhavi lens key utani hii karib hogi. 
isi tarah, ack lens kaa aavardhan dwara diyaa jaataa haye
jahan nakaratmak sanket diyaa jaataa haye, parampara dwara, sakaratmak moolyon key liye ack seedhi vastu aur nakaratmak moolyon key liye ack ulta vastu koo ingit karane key liye. darpanon key samaan, ekal lens dwara utpaadit seedhi chhaviyaan aabhaasi hoti hain jabaki ulte chitra vaastavik hotey hain.
lens una vichalanon seey peedit hotey hain joe chhaviyon aur kendra binduon koo vikrit karate hain. yeye jyaamitiya khamiyon aur prakaash kii vibhinn tarang dairdhya (rangeen vichalan) key liye apavartan key badalate soochkaank donon key kaaran hain.
antarnihit ganit.
ack ganitiya adhyayan key roop mein, jyaamitiya prakashiki atee-javic aanshik vibhedak samikaranon (somerfeld-ranj vidhi) key samadhan key liye ack alp-tarang dairdhya seema key roop mein yaa maxwell key samikaranon (loonberg vidhi) key anusaar kshetra viram key prasaar key guna key roop mein ubharati haye. iss alp-tarang dairdhya seema mein, sthaaniya roop seey samadhan kaa anuman lagaana sambhav haye
jahan sootra _ 15 ack failaav sambandh koo santusht kartaa haye, aur ayam sootra _ 16 dheere-dheere badalata haye. adhik sateek roop seey, agrani crum samadhan roop letaa haye
charan sootra _ 18 koo badey tarang sankhya sootra _ 19, aur aavritti sootra _ 20 koo punarpraapt karane key liye raikhik kiya jaa sakata haye. ayam sootra _ 21 ack parivahan sameekaran koo santusht kartaa haye. chhota mapdand sootra _ 22 atyadhik dolan praarambhik sthitiyon key kaaran drishya mein pravesh kartaa haye. iss prakaar, jaba praarambhik sthitiyaan vibhedak sameekaran key gunank kii tulanaa mein bahut teji seey dolan karati hain, tou samadhan atyadhik dolansheel honge, aur kiranon key saath parivahan kiye jaayenge. yeh maanate hue kii vibhedak sameekaran mein gunank chikane hain, kiranen bhee hongi. dusare shabdon mein, apavartan naheen hotaa haye. iss takneek key liye prerana prakaash prasaar key vishisht paridrishya kaa adhyayan karane seey aatee haye jahaan chhoti tarang dairdhya vaalaa prakaash kiranon key saath yatra kartaa haye joe apane yatra samay koo cumm (cumm yaa jyada) kartaa haye. isake poorna anuprayog key liye sookshm sthaaniya vishleshan seey upkaranon kii aavashyakta hoti haye.
somerfeld-runz vidhi.
shoonya tarang dairdhya kii seema laker jyaamitiya prakashiki key sameekaran praapt karane kii vidhi kaa varnan sabse pahale arnold somerfeld aur jey dwara kiya gayaa thaa. 1911 mein range. unaki vyutpatti peater debby dwara ack maukhik tippani parr adharit thee. ack monochromatic scalar kshetra sootra _ 23 parr vichaar karein, jahan sootra _ 24 vidyut yaa chumbakiya kshetra key kissy bhee ghatak hoe sakata haye aur isaliye falan sootra _ 25 tarang sameekaran koo santusht kartaa haye.
jahan sootra _ 27 key saath sootra _ 28 nirvaat mein prakaash kii gati haye. yahaan, sootra _ 29 madhyam kaa apavartak soochkaank haye. samanyata key nuksan key binaa, aaie humm sameekaran koo badalane key liye sootra _ 30 kaa parichay dein
choonki jyaamitiya prakashiki kaa antarnihit siddhant seema sootra _ 32 mein nihit haye, isaliye nimnalikhit asymptotic shrinkhala maani jaati haye,
sootra _ 34 key badey lekin seemit moolya key liye, shrinkhala alag hoe jaati haye, aur kewal upayukt pahale kuchh shabdon koo rakhane mein savdhani baratani hoti haye. sootra _ 34 key pratyek moolya key liye, 
kissy koo rakhane key liye shabdon kii ack ishtatam sankhya mill sakati haye aur ishtatam sankhya seey adhik sharton koo jodane seey ack kharaab anuman lugg sakata haye. sameekaran mein shrinkhala koo pratisthaapit karate hue aur vibhinn kramon key shabdon koo ekatra karate hue, ack vyakti koo pataa chalata haye
samanya taur parr,
pahala sameekaran ekaatmak sameekaran key roop mein jaanaa jaataa haye, joe ack hamilton-jacoby sameekaran haye, joe ack hamilton-jacoby sameekaran haye, joe udaaharan key liye cartasian nirdeshank mein likhaa jaataa haye.
shesh sameekaran falan sootra _ 40 nirdhaarit karate hain.
loonberg vidhi.
maxwell key samikaranon key samadhanon kii asantulan kii satahon kaa vishleshan karke jyaamitiya prakashiki key sameekaran praapt karane kii vidhi kaa varnan pahali baar 1944 mein rudolf carle loonberg dwara kiya gayaa thaa. yeh vidyut chumbakiya kshetra koo somerfeld-ranj vidhi dwara aavashyak ack vishesh roop mein pratibandhit naheen kartaa haye joe ayam sootra _ 41 aur charan sootra _ 38 koo sameekaran sootra _ 43 koo santusht kartaa haye. yeh sthiti ee dwara santusht haye.jee. samtal tarangen lekin yogaatmak naheen hain.
loonberg key drishtikon kaa mukhya nishkarsh nimnalikhit haih
pramey. maan leejiye kii sootra 44 aur sootra 45 (paraavartak sthiraank sootra 46 aur sootra 47 dwara varnit ack raikhik samasthaanik madhyam mein) mein sameekaran sootra 49 dwara varnit sootra 48 mein ack (gatishil) satah key saath seemit visangatiyaan hain. phir samakalan roop mein maxwell key samikaranon kaa tatparya haye kii sootra 24 ekaatmak sameekaran koo santusht kartaa haih
jahan sootra _ 52 madhyam (gausi ikaaiyaan) key apavartan kaa soochkaank haye.
asantulan kii aisee satah kaa ack udaaharan ack srot seey nikalane vaali praarambhik tarang haye joe ack nishchit samay parr vikiran karna shuru curr detee haye.
iss prakaar kshetra kii asantulan kii satahen jyaamitiya prakashiki tarang morche bunn jaati hain, jinhen sambandhit jyaamitiya prakashiki kshetron key roop mein paribhaashit kiya gayaa haih
way kshetra somerfeld-ranj drishtikon key parivahan samikaranon key anuroop parivahan samikaranon kaa paalan karate hain. loonberg key siddhant mein prakaash kiranon koo asantulan satahon key liye orthogonal prakshepavakra key roop mein paribhaashit kiya gayaa haye aur cumm seey cumm samay key firmate key siddhant kaa paalan karate hue dikhaaya jaa sakata haye iss prakaar maanak prakashiki kii prakaash kiranon key saath una kiranon kii pehchaan sthaapit kii jaa sakati haye.
uparokt ghatnakramon koo anisotropic media key liye saamaanyikrit kiya jaa sakata haye.
loonberg kii pramey kaa pramaan iss baat kii jaanch parr adharit haye kii maxwell key sameekaran samadhanon key asantulan key prasaar koo kaise niyantrit karate hain. buniyaadi takniki paribhasha iss prakaar haih
ack takniki shiksha. maan leejiye kii sootra _ 55 koo spacetime sootra _ 56 mein ack atee surface (ack 3-ayami manifold) honah chaahiye, jiss parr ack yaa adhik sootra _ 44, sootra _ 45, sootra _ 46, sootra _ 47, ack seemit visangati haye. phir atee satah key pratyek bindu parr nimnalikhit sootra pakadate hainh
jahan sootra _ 65 prachaalak sootra _ 66-sthaan (pratyek nishchit sootra _ 67 key liye) mein kaary kartaa haye aur varg koshthak asantulan satah key donon taraf key moolyon mein antar koo darshaate hain (ack manmaane lekin nishchit parampara key anusaar sthaapit, ee.jee. seey" ghataai jaa rahee maatraon kii disha mein ingit karane vaalaa pravanata sootra _ 68).
pramaan kaa rekhaachitra. sroton (gausi ikaaiyon) seey door maxwell key samikaranon seey shuru karenh
sootra _ 56 mein stokes pramey kaa upayog karke uparokt samikaranon mein seey pahale seey nishkarsh nikala jaa sakata haye kii sootra _ 56 mein kissy bhee domen sootra _ 74 key liye ack peacevise smooth (3-dimensional) seema sootra _ 76 key saath nimnalikhit sach haih
jahan sootra 78, sootra 76 key 3dee slies sootra 81 parr baahari ikai samanya sootra 79 kaa prakshepan haye, aur sootra 82 sootra 76 parr aayatan 3-roop haye. isi tarah, shesh maxwell key samikaranon seey nimnalikhit sthaapit hotaa haih
abb sootra 76 key manmaane chhote upa-satah sootra _ 87 parr vichaar karke aur sootra _ 56 mein sootra _ 87 key aspas key chhote pados sthaapit karke, aur tadnusar uparokt samakalan koo ghataakar, koee praapt kartaa haih
jahan sootra _ 95 4d sootra _ 96-sthaan mein pravanata koo darshaata haye. aur choonki sootra _ 87 manmana haye, isaliye samakalan 0 key barabar honah chaahiye joe lemma koo saabit kartaa haye.
abb yeh dikhaana aasaan haye kii jaise-jaise way ack nirantar madhyam key madhyam seey prasaar karate hain, asantulan satahen ekaatmak sameekaran kaa paalan karati hain. vishesh roop seey, yadi sootra 98 aur sootra 99 nirantar hain, tou sootra 100 aur sootra 101 kii visangatiyaan santusht karati hainh sootra 102 aur sootra 103. iss mamle mein lemma key antim dou samikaranon koo iss prakaar likhaa jaa sakata haih
sootra _ 68 key saath dusare sameekaran key cross utpaad koo lete hue aur pahali paidawar koo pratisthaapit karate hueh
sootra 99 kii nirantarta aur lemma key dusare sameekaran kaa tatparya haih sootra 109, isaliye, satah sootra 110 parr padey binduon key liye "kewal":
bhautik vichaaron key kaaran koee bhee samanyata key nuksan key binaa maan sakata haye kii sootra _ 112 nimnalikhit roop kaa haih
sootra _ 113, i.ee. ack 2d satah antariksh key madhyam seey aage badh rahee haye, sootra _ 24 kii star satahon key roop mein pratiroopit haye. (ganitiya roop seey sootra _ 24 maujood haye yadi antarnihit falan pramey dwara sootra _ 116 haye.)
sootra _ 24 key sandarbh mein likhaa gayaa uparokt sameekaran bunn jaataa haih
aaee.ee.,
joe ekaatmak sameekaran haye aur yeh sabhi sootra _ 120, sootra _ 121, sootra _ 122 key liye dhaaran kartaa haye, kyonki charr sootra _ 67 anupasthit haye. snell key niyam aur fresnell sootra jaise prakashiki key anya niyamon koo sootra _ 98 aur sootra _ 99 mein visangatiyon parr vichaar karke isi tarah praapt kiya jaa sakata haye.
chaar-vaahak sanketan kaa upayog karke samanya sameekaran.
vishesh saapekshata mein upayog kiye jaane vaale chaar-vector sanketan mein, tarang sameekaran koo iss prakaar likhaa jaa sakata haye
aur pratisthaapan sootra _ 127 kii or leey jaataa haye
isaliye acon sameekaran dwara diyaa jaataa haye
ack baar jaba uparokt sameekaran koo hull karke ack samkon paaya jaataa haye, tou tarang chaar-vaahak koo yahaan seey paaya jaa sakata haye