vivrtan

ek vargaakaar dvaarak (aperture) se vivrtan ke parinaamasvaroop parde par nirmit vivrtan paitarn

jab prakaash ya dhvani tarange kisi avarodh se takaraati hain, to ve avarodh ke kinaaron par mud jaati hain aur avarodhak ke ki jyaamitiya chhaaya mein pravesh kar jati hain. tarango ke is prakaar mudne ki ghatna ko vivrtan (Diffraction) kehte hain. aisa paaya gaya hai ki laghu aakaar ke avarodhon se takaraane ke baad tarangein mud jaateen hain tatha jab laghu aakaar ke chhidron (openings) se hokar tarang gujarati hai to yeh fail jaati hai. sabhi prakaar ki tarangon se vivrtan hota hai (dhvani, jal tarang, vidyutachumbakeeya tarang aadi).

yadi kisi prakaashotpaadak srot aur parde ke beech koi apaaradarshak vastu rakh di jaae, to parde par vastu ki chhaaya ban jaati hai. bahudha chhaaya ka kinaara teekshn (sharp) hota hai aur uske chaaron or parde ka bhaag samaan roop se prakaashit rahata hai. yadi prakaashotpaadak srot binduvat chhota ho, to dhyaan se dekhne par chhaaya ka kinaara teekshn naheen paaya jaata hai. kinaare par prakaash aur andhakaar (brightness and darkness) ki dhaariyaaain dikhaai padti hain. aisa maaloom hota hai ki prakaash ki kirnein mudkar jyaamiteeya chhaaya ki seema ke bheetar tak pahunch gayi hain. is ghatna ko prakaash ka vivrtan kehte hain. chhaaya ke kinaare-kinaare jo dhaariyaaain banti hain, unhein vivrtan paitarn (Diffraction Pattern) kaha jaata hai. vivrtan ki jaankaari se poorv yahi maana jaata tha ki kisi ek maadhyam mein prakaash seedhi rekhaaon mein chalta hai. kintu vivrtan ki vyaakhya prakaash ke saral raikhik gaman ke aadhaar par naheen ki ja sakti hai. sarvapratham nyootan (Newton), grimaaldi (Grimaldi) aur ti. yang (T. Young) ne is ghatna par dhyaan diya tha. nyootan aur grimaaldi prakaash ke kanika siddhaant (Corpuscular Theory) ke pravartak aur anuyaayi the, at: unhonne vivrtan ki ghatna ko isi aadhaar par samajhne ka asafal prayaas kiya. baad mein krishchiyn haaigeinj ne prakaash ke tarang siddhaant ka pratipaadan kiya aur A. J. frenel (A. J. Fresnel) tatha fraaunahofar (Fraunhofer) ne isi siddhaant ke aadhaar par vivrtan tatha vivrtan se sambandhit anya ghatnaaon ko safalta poorvak samajhaaya.

jab prakaash ke maarg mein gol chhed, aayataakaar rekhaachhidr, kisi vastu ki teekshn kor (edge) ya maheen taar rakha jaata hai, tab pratyek dasha mein bhinn prakaar ke vivrtan paitarn bante hain. vivrtan ki sabhi ghatnaaon ko do vibhaagon mein baaainta ja sakta hai :

(1) fraaunahofar vivrtan (Fraunhofer Diffraction) aur (2) frenel vivrtan (Fresnel Diffraction).

jab prakaashasrot aur parda vivrtak vastu se atyant door hote hain, arthaat vivrtak par samatal tarangaagr (plane wavefront) apaatit hota hai, tab vivrtan paitarn ko fraaunahofar paitarn aur ghatna ko fraaunahofar vivrtan kaha jaata hai. jab srot, parda, ya ye donon, vivrtak vastu se niyat (finite) doori par hote hain, arthaat vivrtak par goleeya ya belanaakaar tarangaagr aapatit hota hai, tab vivrtan ki ghatna ko frenel vivrtan kaha jaata hai. frenel vivrtan dekhna apekshaakrut saral hota hai, kintu ise samajhna kathin hota hai. fraaunahofar vivrtan dekhne ke liye vishesh prakaar ki vyavastha karni padti hai, jisse samatal tarangaagr praapt ho. vivrtan ke baad use pun: focus karne ki vyavastha karni padti hai, kintu iska siddhaant samajhna bahut saral hai.

fronahofar vivrtan:- esa vivrtan jismein prakaash shrot tatha parda avarodhak se anant doori par ho.

akele rekhaachhidr ka vivrtan paitarn (Diffraction pattern of single slit)

sodiym laip se peele rang ka ekavarni prakaash (monochromatic light) praapt hota hai. ek leins ki sahaayata se is prakaash ko ek kaale pardein mein kate hue atyant sainkare rekhaachhidr (slit) par daala jaae, to yahi rekhaachhidr swayam ek prakaash srot ka kaam deta hai. ab is rekhaachhidr ke aage leins lagaakar samaantar kirnapunj ko ek doosare rekhaachhidr par daala jaae tatha is rekhaachhidr ke peechhe safed parda rakha jaae, to pardein par doosare rekhaachhidr ka vivrtan paitarn ban jaata hai. is paitarn ke beech mein atyant teevr band (intense band) ya patti hoti hai. is patti ke donon or apekshaakrut bahut kam teevrata ki aur bhi pattiyaaain pai jaati hain. beechavaali patti ko mukhya uchchishth (Principal Maxima) tatha anya pattiyon ko dviteeyak uchchishth (Secondary Maxima) kehte hain.

vivrtan greting (Diffraction Grating)

do sameepavarti rekhaachhidron ka vivrtan paitarn ek rekhaachhidr ke vivrtan paitarn se kuchh bhinn hota hai. ek rekhaachhidr ke paitarn mein jahaaain jahaaain uchchishth milta hai, do rekhaachhidr ke paitarn mein unheen sthaanon par kai dhaariyaaain banti hain, jo pehle ke baindon ki apeksha adhik patali aur teekshn hoti hain. jyon-jyon rekhaachhidron ki sankhya badhti jaati hai, dviteeyak uchchishth ki dhaariyaaain ksheen hoti jaati hain aur mukhya uchchishth ki dhaariyaaain atyant teekshn hoti jaati hain. rekhaachhidron ki chaudaai tatha unki paarasparik doori bhi in dhaariyon ki teekshnata ko bahut prabhaavit karti hai. sheeshe ki samatal patti par heere ki kani se rekhaaeain kheench di jaaeain, to pratyek do rekha ke beech ka paaradarshak sthaan rekhaachhidr ka kaam karta hai. aise hi rekhaachhidron ke samooh ko greinting kehte hain. greting ka aavishkaar fraaunahofar ne kiya tha. unhonne do skroo ke oopar maheen taar lapetakar greting banaaya tha. pratyek do taaron ke beech ka sthaan rekhaachhidr ka kaam karta hai. aage chalakar unhonne kaaainch ke plate par rekhaaeain kheenchakar greting banaaya. rolaind ne 1882 E. mein greting ki rekhaaeain banaanevaali machine banaai. aajkal achhi masheenon dvaara ek inch par 30,000 ya 40,000 tak rekhaaeain kheenchi jaati hain.

yadi kisi prakaashasrot ke sammukh leins rakhakar, ekavarni samaantar kirnon ko ek greting par daala jaae, to isse praapt vivrtan mein ek doosari se door door kai teekshn rekhaaeain pai jaati hain. ye rekhaaeain vaastav mein rekhaachhidr srot ka vivrtan binb hoti hain. beech ki sabse teevr rekha ko shoonya koti (Zero order) ki rekha kehte hain. iske donon or pehli, doosari, teesari aadi rekhaaeain kramash: pratham, dviteeya tatha truteeya koti ki rekhaaeain kahalaati hain. yadi greting par shvet prakaash daala jaae, to shoonya koti ki rekha shvet hoti hai, kintu anya koti ki rekhaaon sthaan par spectrum praapt hote hain. inhein kramash: pratham, dviteeya, truteeya aadi koti ke spectrum kaha jaata hai. yadi greting se vivrtit honevaale prakaash ka tarangadairdhya l, aapatit tarangaagr ka aapatan kon i aur vivrtan kon q ho tatha kinheen do sameepasth rekhaachhidron ke madhyabinduon ki paarasparik doori d ho, to

d (sin-i + sin q) = n l hota hai. n spectrum ki koti (order) ka dyotak hai.

oopar jis greting ka vivran diya gaya hai, use samatal vivrtan greting kehte hain. yadi vakr sheeshe par ailuminiym ki kalai kar di jaae aur usi par heere ki kani se rekhaaeain khurach di jaaeain, to pratyek do rekhaaon ke beech ka bhaag ek nanhein paraavarti darpan ka kaam karta hai. in bhaagon se paraavartit tarangon ke vyatikran se bhi vivrtan paitarn banta hai. is greting ko avatal greting (Concave grating) kehte hain. iska aavishkaar rolaind (Rowland) ne kiya tha. avatal greting avatal darpan ka bhi kaam karta hai. at: vivrtit kirnon ko foks karne ke liye leins ka prayog naheen karna padta hai.

spektramiki (spectroscopy) mein spectrum praapt karne ke liye vakr greting se bade upayogi spektrograaf banaae gaye hain. vakr greting ke liye bhi tarangadairdhya ka sootr d (sin i + sin q) = n l hi hota hai. do vibhinn varnon ki rashmiyon (l1, l2) ko ek doosare se pruthak karne ki kshamata ko greting ki varnavikshepan kshamata (Dispersive Power) kaha jaata hai. yadi l1- l2 = Dl ho aur inke vivrtan kon kramash: q1 aur q2 hon tatha q1 - q2 = Dq ho, to greting ki varn vikshepan kshamata hoti hai. tanragadairghya ke sootr se iska maan hota hai. kramash: uchchatar koti mein varn vikshepan kshamata badhti jaati hai. yadi l aur l+dl do atyant sameepavarti vikirn (radiations) hon aur greting dvaara inko ek doosare se alag-alag dekha ja sake to dl ko greting ki vibhedan kshamata (resolving power) kehte hain. N greting par bani hui kul rekhaaon (ya rekhaachhidron) ki sankhya hai. kramash: uchchtar koti mein vibhedan kshamata bhi badhti jaati hai.

frainel vivrtan :-esa vivrtan jis mein prakaash shrot tatha parda avarodhak ya dvaarak se seemeet doori par ho.

chhaaya ka banana

chhaaya ke kinaare par vivrtan paitarn ka banana prakaash ke saral raikhik gaman se naheen samajhaaya ja sakta hai. ise samajhaane ke liye frainel ne tarang siddhaant ka upayog kiya. kisi tarangaagr ke vibhinn binduon ka prabhaav samajhaane ke liye unhonne ardh kaal jon (Half Period Zones) ka siddhaant pratipaadit kiya. is siddhaant ke aadhaar par banaaya gaya jon plate leins ki bhaaainti kaam karta hai aur frenel ke siddhaant ki pushti karta hai.

gol chhidr se vivrtan

yadi kisi atyant chhote chhidr par ekavarni samatal tarangaagr aapatit hota ho, to pardein par iska vivrtan paitarn ban jaata hai. is paitarn mein vruttaakaar dhaariyaaain (circular fringes) pai jaati hain. sabse baahari dhaari sabse adhik moti hoti hai aur bheetari dhaariyaaain kramash: patali hoti hain. frenel ke ardhakaal jon ke aadhaar par is vivrtan ki vyaakhya ki ja sakti hai.

yadi chhidr ka aakaar pratham ardhakaal jon ke baraabar ho aur paitarn ke kendra tatha chhidr ki paridhi ki dooriyon ka antar (2m+1) l/2 ho, to paitarn ka kendra prakaashit hota hai. yadi parde se chhidr ki doori sthir rakhakar chhidr ka aakaar badhaate jaaeain, to yeh kendra kramash: prakaashit (bright) aur aprakaashit (dark) hota hai. jab chhidr ka aakaar (2m+1) ardhakaal-jon samaavisht karta hai, to paitarn ka kendra chamakeela hota hai aur jab chhidr mein 2m ardh-kaal-jon samaavisht hote hain, to kendra kaala hota hai. chhidr ko sthir rakhakar pardein ko usase sameep ya door laane par bhi kendra par parivartan hota hai. yadi paitarn ke kendra se chhidr ke kendra aur chhidr ki paridhi ki dooriyon ka antar (2 m+1) l/2 ho, to kendra chamakeela, anyatha kaala, hota hai.

gol disk ke vivrtan paitarn ke kendra par sarvada ek chamakeeli bindi banti hai.

kisi prakaasheeya yantr dvaara kisi bindu srot ka binb (image) vaastav mein us yantr ke dvaarak (aperture) se hokar jaanevaali tanragon ka vivrtan paitarn hota hai. yadi do bindu srot atyant paas paas hon, to yantr dvaara pratyek ka ek-ek vivrtan paitarn banta hai. chooainki sabhi prakaasheeya yantron mein vartul dvaarak (circular aperture) hota hai, at: bindu sroton ke vivrtan paitarn mein vartul bindu (spot) banta hai aur uske kinaare kinaare kai vartul valaya (rings) hote hain. yantr ka dvaarak jitna hi bada hota hai, vivrtan paitarn utane hi chhote bante hain. yadi prakaasheeya yantr dvaara do atyant sameepasth bindu sroton ke vivrtan paitarn itne chhote aur spasht banein ki ek ka keindreeya mahattam (central maximum) prakaashit bhaag doosare ke sarvapratham nyoonatam (first minimum) prakaashit bhaag par pade, to donon ke keindreeya bindu (spots) spasht dekhein ja sakte hain. prakaasheeya yantr ki is kshamata ko vibhedan kshamata (Resolving Power) kehte hain.

bahudha aakaash mein baadalon ki upasthiti ke samay soorya athva chandrama ke chaaron or ek chamakeela ghera dikhaai padta hai. ise kireet kehte hain. paani ki nanheen booaindon dvaara prakaash ka vivrtan hone se hi kireet bante hain. spasht kireet ke liye nanheen booaindon ka samaakaar hona aavashyak hota hai. ye booainde jitni hi adhik chhoti hoti hain kireet ka vyaas utana hi bada hota hai. ti yang (T. Young) ne kireeton ka vyaas naapakar jalakanon ke vyaas ki ganana karne ke liye yantr banaaya tha, jise tantumaapi (Eriometer) kehte hain.

vivrtan aur vyatikran mein siddhaantat: koi bhed naheen hai. tab bhi bahudha yeh kaha jaata hai ki vyatikran mein kuchh niyat sankhya ke prakaashapunjon ka adhyaaropan (superposition) hone se tarang aayaam (wave amplitude) ke pratyek atisookshm khandon (elements) ke prabhaav ka samaakalan (integrate) karke tarang ka aayaam gyaat kiya jaata hai. ek se adhik rekhaachhidron ka vivrtan paitarn, vivrtan aur vyatikran ke sanyukt prabhaav se, banta hai. sankshep mein; vivrtan, vyatikran ka hi kinchit klisht roop hai.

• Do Sensors “aOutresolve” Lenses?; on lens and sensor resolution interaction.
• Diffraction and acoustics.
• Diffraction in photography.
• On Diffraction at MathPages.
• Diffraction pattern calculators at The Wolfram Demonstrations Project
• Wave Optics – A chapter of an online textbook.
• 2-D wave Java applet – Displays diffraction patterns of various slit configurations.
• Diffraction Java applet – Displays diffraction patterns of various 2-D apertures.
• Diffraction approximations illustrated – MIT site that illustrates the various approximations in diffraction and intuitively explains the Fraunhofer regime from the perspective of linear system theory.
• Gap Obstacle Corner – Java simulation of diffraction of water wave.
• Google Maps – Satellite image of Panama Canal entry ocean wave diffraction.