I\u015eI\u011eIN KIRINIMI<\/p>\n
K\u0131r\u0131n\u0131m olay\u0131 genel anlamda Leonardo da Vinci taraf\u0131ndan bilinmesine ra\u011fmen \u0131\u015f\u0131\u011f\u0131n k\u0131r\u0131n\u0131m\u0131 ilk olarak Grimaldi (Fren\u00e7eska Grimaldi) taraf\u0131ndan g\u00f6zlenmi\u015f ve etrafl\u0131ca tasvir olunmu\u015ftur. Grimaldi’ nin k\u0131r\u0131n\u0131m hakk\u0131ndaki yaz\u0131lar\u0131, 1665 y\u0131l\u0131nda bas\u0131lan kitab\u0131nda mevcuttur.
\nK\u0131r\u0131n\u0131m olay\u0131n\u0131n dalga teorisi a\u00e7\u0131s\u0131ndan izah\u0131 1818 y\u0131l\u0131nda ilk kez Fresnel taraf\u0131ndan yap\u0131lm\u0131\u015ft\u0131r. Fresnel dalgalar\u0131n \u00fcst \u00fcste binerek giri\u015fim olu\u015fturma imk\u00e2n\u0131n\u0131 dikkate alarak Huygens prensibini geli\u015ftirmi\u015f ve yeni bir prensip ortaya koymu\u015ftur. K\u0131r\u0131n\u0131m olay\u0131n\u0131n incelenmesinde bu yeni prensip Huygens-Fresnel prensibi olarak adland\u0131r\u0131lm\u0131\u015ft\u0131r. Sonralar\u0131 Kirchhoff k\u0131r\u0131n\u0131m teorisinin matematik temelini ortaya koymu\u015ftur.
\nBiz, k\u0131r\u0131n\u0131m olay\u0131n\u0131 lineer optik a\u00e7\u0131s\u0131ndan inceliyece\u011fiz. Fazla \u015fiddetli \u0131\u015f\u0131k – ak\u0131mlar\u0131n\u0131n yay\u0131lmas\u0131na ba\u011fl\u0131 olarak lineer opti\u011fin temel kanunlar\u0131nda meydana gelen baz\u0131 sapmalar hakk\u0131nda ise k\u0131sa izahlarla yetinece\u011fiz.<\/p>\n
6.1. HUYGENS-FRESNEL PRENS\u0130B\u0130
\nDalga cephesinin belirli bir andaki durumu bilinirse, Huygens’in dalga prensibi esas al\u0131narak sonraki istenilen anlarda dalga cephesi; dolay\u0131s\u0131yla da \u0131\u015f\u0131nlar\u0131n do\u011frultulan bulunabilir. I\u015f\u0131n\u0131n yay\u0131lma do\u011frultusu bu yolla bulundu\u011funda \u015f\u00f6yle bir sonu\u00e7 elde edilmi\u015ftir. Saydam olmayan ekran \u00fczerindeki delikten veya yar\u0131ktan \u0131\u015f\u0131k ge\u00e7ince geometrik yay\u0131lma do\u011frultusundan (bir cins ortamda do\u011fru yol boyunca yay\u0131lma do\u011frultusundan) bir sapma g\u00f6zlenir. \u0130\u015fte \u0131\u015f\u0131\u011f\u0131n kar\u015f\u0131s\u0131na \u00e7\u0131kan engelleri b\u00f6yle ge\u00e7mesine k\u0131r\u0131n\u0131m denir.
\nK\u0131r\u0131n\u0131m probleminin tam \u00e7\u00f6z\u00fclmesi i\u00e7in \u0131\u015f\u0131\u011f\u0131n; engeli ge\u00e7tikten sonra \u015fiddetini ve yeni yay\u0131lma do\u011frultular\u0131n\u0131, dolay\u0131s\u0131yla, k\u0131r\u0131n\u0131m a\u00e7\u0131lar\u0131n\u0131 belirlemek gerekir. Sadece Huygens prensibi ile bu problem \u00e7\u00f6z\u00fclemez. Ancak bu problem, giri\u015fim ile desteklenen Huygens-Fresnel prensibi yard\u0131m\u0131 ile \u00e7\u00f6z\u00fclm\u00fc\u015ft\u00fcr. Huygens-Fresnel prensibi, \u0131\u015f\u0131\u011f\u0131n bir cins ortamda do\u011fru yol boyunca yay\u0131lmas\u0131n\u0131 dalga teorisi \u00e7er\u00e7evesinde a\u00e7\u0131klamaya da imk\u00e2n verir.<\/p>\n
Huygens-Fresnel Prensibi
\nFresnel’e g\u00f6re, k\u0131r\u0131n\u0131m an\u0131nda meydana gelen ikinci (yard\u0131mc\u0131) yar\u0131 k\u00fcresel elemanter dalgalar uyumlu oldu\u011fundan ekran\u0131n her noktas\u0131nda sonu\u00e7 \u0131\u015f\u0131k \u015fiddetini bulurken bu \u015fekilde olu\u015fmu\u015f ikinci dalgalar\u0131n giri\u015fimini nazara almak gerekir. Fresnel; \u0131\u015f\u0131k kayna\u011f\u0131n\u0131 kendi etraf\u0131nda istenilen \u015fekle sahip ayd\u0131nlanm\u0131\u015f kapal\u0131 bir y\u00fczeyle temsil etmeyi teklif etmi\u015ftir. Kapal\u0131 y\u00fczeyin her elemanter hisseleri kar\u015f\u0131l\u0131kl\u0131 uyumlu oldu\u011fundan ekran\u0131n her belirli bir noktas\u0131nda sonu\u00e7 \u015fiddeti bulurken b\u00fct\u00fcn elemanter hisselerin tesirlerini, onlar\u0131n genlik ve fazlar\u0131n\u0131 dikkate alarak toplamak gerekir.
\nS kayna\u011f\u0131ndan \u00e7\u0131kan l dalga boylu \u0131\u015f\u0131k dalgas\u0131n\u0131n bir cins ortamda B noktas\u0131na taraf yay\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6z\u00f6n\u00fcne alal\u0131m (\u015fekil 6.1). Genel halde kayna\u011f\u0131, istenilen \u015fekilli kapal\u0131 bir y\u00fczeyle temsil edebiliriz. Basit hal i\u00e7in b\u00f6yle bir kapal\u0131 y\u00fczey olarak; merkezi, kaynak olan R yar\u0131\u00e7apl\u0131 k\u00fcre y\u00fczeyini (dalga cephesini) g\u00f6z\u00f6n\u00fcne alal\u0131m.
\nHuygens-Fresnel prensibine g\u00f6re ayd\u0131nlanm\u0131\u015f kapal\u0131 y\u00fczeyin (dalga cephesinin) her hissesi ikinci kaynaklar\u0131n (yard\u0131mc\u0131 kaynaklar\u0131n) merkezi olarak kabul olunabilir. \u00dczerinde Mj noktas\u0131n\u0131n yerle\u015fti\u011fi Dsjy\u00fczeyinden \u00e7\u0131kan \u0131\u015f\u0131k dalgas\u0131n\u0131n B noktas\u0131nda meydana getirdi\u011fi titre\u015fim,
\nEj = f(aj) Dsjcos(wt \u2013 kr – j0) = E0j cos(wt \u2013 kr – j0) (6.1)
\n\u015feklinde yaz\u0131labilir. Burada;
\nE0j = f(aj) Dsj<\/p>\n
k\u00fc\u00e7\u00fck Dsj y\u00fczeyi taraf\u0131ndan B noktas\u0131nda meydana getirilen titre\u015fimin genli\u011fi, EO de\u011feri; Dsjkayna\u011f\u0131n\u0131n birim uzakl\u0131ktaki genli\u011fi, jo ba\u015flang\u0131\u00e7 faz\u0131, rj kaynak olarak kabul etti\u011fimiz Dsjy\u00fczeyinden B noktas\u0131na kadar olan uzakl\u0131k, aj kaynaktan seyir noktas\u0131na \u00e7izilen \u00e7izgi ile bu kaynak (Dsjy\u00fczeyi) y\u00fczeyinin normali aras\u0131ndaki a\u00e7\u0131 (k\u0131r\u0131n\u0131m a\u00e7\u0131s\u0131) ve f(aj) yard\u0131mc\u0131 dalga genli\u011finin do\u011frultu ile ilgisini karakterize eden katsay\u0131d\u0131r.
\nDsjy\u00fczeyini \u00f6yle k\u00fc\u00e7\u00fck se\u00e7meliyiz ki, bu y\u00fczey \u00fczerinde aj ve rj pratik olarak sabit kals\u0131n. Fresnel’e g\u00f6re f (aj), a = 0 oldu\u011funda maksimum de\u011ferini al\u0131rken, a b\u00fcy\u00fcyerek ap\/2 oldu\u011funda. f(aj) de k\u00fc\u00e7\u00fclerek s\u0131f\u0131r de\u011ferini al\u0131r. S kayna\u011f\u0131 ile B noktas\u0131 aras\u0131nda yerle\u015ftirilmi\u015f saydam olmayan ekran \u00fczerindeki t\u00fcm noktalarda (delik y\u00fczeyi hari\u00e7) yard\u0131mc\u0131 dalga genlikleri s\u0131f\u0131rd\u0131r. Ekran \u00fczerindeki delik a\u00e7\u0131ld\u0131\u011f\u0131nda, yard\u0131mc\u0131 kaynak, y\u00fczeyin delik b\u00f6lgesinde istenilen (ama\u00e7la ilgili ola\u00adrak) \u015fekilde se\u00e7ilmi\u015f y\u00fczeyden ve saydam olmayan ekran\u0131n (delik hari\u00e7) kalan y\u00fczeyinden olu\u015fur.
\nI\u015f\u0131\u011f\u0131n ekran maddesi ile kar\u015f\u0131l\u0131kl\u0131 etkisi nazara al\u0131nmaz. Yani, delik b\u00f6lgesine ^ uygun gelen genlik gerek bu halde, gerekse saydam olmayan ekran olmasada ayn\u0131d\u0131r. Demek ki, saydam olmayan ekran\u0131n rol\u00fc sadece yard\u0131mc\u0131 kapal\u0131 y\u00fczeyin belirli k\u0131sm\u0131ndan (bak\u0131lan halde delik b\u00f6lgesi hari\u00e7 kalan k\u0131s\u0131mdan) seyir ekran\u0131na gelen \u0131\u015f\u0131\u011f\u0131 engellemek i\u00e7indir. Asl\u0131nda problemin hassas c\u00fcz\u00fcm\u00fc i\u00e7in ekran maddesinin fiziksel \u00f6zellikleri dikkate al\u0131narak s\u0131n\u0131r \u015fartlar\u0131 belirtilmelidir.<\/p>\n
Sonu\u00e7 Genli\u011fin Hesaplanmas\u0131 I\u015eI\u011eIN KIRINIMI K\u0131r\u0131n\u0131m olay\u0131 genel anlamda Leonardo da Vinci taraf\u0131ndan bilinmesine ra\u011fmen \u0131\u015f\u0131\u011f\u0131n k\u0131r\u0131n\u0131m\u0131 ilk olarak Grimaldi (Fren\u00e7eska Grimaldi) taraf\u0131ndan g\u00f6zlenmi\u015f ve etrafl\u0131ca tasvir olunmu\u015ftur. Grimaldi’ nin k\u0131r\u0131n\u0131m hakk\u0131ndaki yaz\u0131lar\u0131, 1665 y\u0131l\u0131nda bas\u0131lan kitab\u0131nda mevcuttur. K\u0131r\u0131n\u0131m olay\u0131n\u0131n dalga teorisi a\u00e7\u0131s\u0131ndan izah\u0131 1818 y\u0131l\u0131nda ilk kez Fresnel taraf\u0131ndan yap\u0131lm\u0131\u015ft\u0131r. Fresnel dalgalar\u0131n \u00fcst \u00fcste binerek giri\u015fim olu\u015fturma …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1407,1403],"tags":[6839,6840,6837,6838],"class_list":["post-2782","post","type-post","status-publish","format-standard","hentry","category-fen-ve-teknoloji-odevleri","category-odevler","tag-huygens-prensibi","tag-huygens-fresnel-prensibi","tag-isigin-kirinimi","tag-leonardo-da-vinci"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/2782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=2782"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/2782\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=2782"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=2782"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=2782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nS kayna\u011f\u0131ndan \u00e7\u0131kan \u0131\u015f\u0131\u011f\u0131 r yar\u0131\u00e7apl\u0131 deli\u011fi olan saydam olmayan ekran y\u00fczeyine y\u00f6neltelim. Delikte k\u0131r\u0131n\u0131m yapt\u0131ktan sonra B noktas\u0131na taraf yay\u0131lan \u0131\u015f\u0131\u011f\u0131 g\u00f6z\u00f6n\u00fcne alal\u0131m
\nB noktas\u0131nda sonu\u00e7 genli\u011fi bulmak i\u00e7in ifadesi ile belirtilen titre\u015fimleri a y\u00fczeyi boyunca toplamal\u0131y\u0131z. Genellikle, bu problemin \u00e7\u00f6z\u00fcm\u00fc, matematik \u00e7\u00f6z\u00fcm\u00fcn fazla kar\u0131\u015f\u0131k olmas\u0131ndan \u00f6t\u00fcr\u00fc s\u0131k\u0131nt\u0131l\u0131d\u0131r. Bu s\u0131k\u0131nt\u0131y\u0131 ortadan kald\u0131rmak amac\u0131yla Fresnel, bant metodu denilen bir metod teklif etmi\u015ftir. Fresnel’in bant metoduna g\u00f6re, dalga cephesi (ayd\u0131nlanm\u0131\u015f y\u00fczey); merkezi Mo (SB do\u011fru \u00e7izgisi ile s y\u00fczeyinin kesim noktas\u0131) noktas\u0131 olmak \u00fczere s y\u00fczeyi halka \u015fekilli bantlara b\u00f6l\u00fcn\u00fcr. B\u00f6l\u00fcnme \u015fartlar\u0131na g\u00f6re kom\u015fu bantlar\u0131n d\u0131\u015f s\u0131n\u0131rlar\u0131n\u0131 B noktas\u0131 ile birle\u015ftiren do\u011frular\u0131n uzunluklar\u0131 fark\u0131, yar\u0131m dalga boyuna e\u015fit olmal\u0131d\u0131r. Yani;
\nM1B \u2013 M0B = M2B \u2013 M1B = … = (Mj – Mj-1) B = .. = (6.2)
\n\u015fart\u0131 yerine getirilmelidir. Dalga cephesini b\u00f6yle halka bantlara b\u00f6lmek i\u00e7in; merkezi; B noktas\u0131nda olan, yar\u0131\u00e7aplar\u0131 ise s\u0131ras\u0131yla,
\nr0, r0 + , \u2026., r0 + j
\nolan yar\u0131 k\u00fcre y\u00fczeyleri \u00e7izmek gerekir. (6.1) ifadesinden g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi j. Fresnel band\u0131n\u0131n B noktas\u0131nda meydana getirdi\u011fi titre\u015fimin genli\u011fi,
\nEoj = f(aj) Dsj (6.3)
\nolur. Demek ki, j. band\u0131n seyir noktas\u0131ndaki genli\u011fi; j. band\u0131n Dsj alan\u0131, aj k\u0131r\u0131n\u0131m a\u00e7\u0131s\u0131 ve j. bantla B noktas\u0131 aras\u0131ndaki rj uzakl\u0131\u011f\u0131 ile ilgilidir. Kom\u015fu halka bantlardan B seyir noktas\u0131na gelen \u0131\u015f\u0131nlar\u0131n yollar fark\u0131 l\/2′ ye e\u015fit oldu\u011funda bu kom\u015fu titre\u015fimler B noktas\u0131na z\u0131t fazlarla gelir. Demek ki, kom\u015fu genlikler toplama i\u015flemine z\u0131t i\u015faretlerle gireceklerdir. S\u00f6ylediklerimiz dikkate al\u0131n\u0131rsa; B noktas\u0131nda s y\u00fczeyini olu\u015fturan t\u00fcm Fresnel bantlar\u0131n\u0131n sonu\u00e7 genli\u011fi,
\nE0 = E01 \u2013 E02 + E03 \u2013 E04 + \u2026 E0i (6.4)
\nolur. Burada, j tek olursa E0; \u00f6n\u00fcndeki i\u015faret pozitif, j \u00e7ift olursa negatif olacakt\u0131r.
\nSonu\u00e7 genli\u011fi bulmak i\u00e7in numaralar\u0131n artmas\u0131 ile ilgili olarak bant genliklerinin de\u011fi\u015fimine bakal\u0131m ve genlik birka\u00e7 tane bilinmeyenle ilgili oldu\u011fundan bu ilgiyi s\u0131ras\u0131yla inceleyelim:
\n1. aj’nin s\u0131f\u0131rdan p\/2’ye kadar b\u00fcy\u00fcmesi ile f(aj) katsay\u0131s\u0131 (bant\u0131n meyil katsay\u0131s\u0131) kendisinin m\u00fcmk\u00fcn olan en b\u00fcy\u00fck de\u011ferinden s\u0131f\u0131ra kadar k\u00fc\u00e7\u00fcl\u00fcr. Demek ki, bant numaras\u0131 b\u00fcy\u00fcd\u00fc\u011f\u00fcnde, band\u0131n meyil katsay\u0131s\u0131na ba\u011fl\u0131 olarak genlik k\u00fc\u00e7\u00fcl\u00fcr.
\n2. (6.3) ifadesinden g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi genlik, rj nin b\u00fcy\u00fcmesine ba\u011fl\u0131 olarak k\u00fc\u00e7\u00fcl\u00fcr.
\n3. Genlik, bant alan\u0131n\u0131n b\u00fcy\u00fckl\u00fc\u011f\u00fc ile do\u011fru orant\u0131l\u0131d\u0131r. Fakat biz, bant alan\u0131n\u0131n numara ile ilgisini hen\u00fcz bilmiyoruz. Problemin \u00e7\u00f6z\u00fcm\u00fc i\u00e7in alan b\u00fcy\u00fckl\u00fcy\u00fcn\u00fcn bant numaras\u0131 ile ilgisini belirlemeliyiz. Kolayca ispat edilebilir ki, belirli bir yakla\u015f\u0131m i\u00e7inde bant alanlar\u0131 numaralarla ilgili olmay\u0131p sabit kal\u0131r. Yani,
\nDs1 = Ds2 = Ds3 = \u2026 = Ds
\nd\u0131r. Yukar\u0131da yaz\u0131lan e\u015fitli\u011fin varl\u0131\u011f\u0131n\u0131 isbat etmek amac\u0131yla j. band\u0131n {burada j istenilen tamsay\u0131 de\u011ferleridir ve kaynakla seyir ekran\u0131 aras\u0131nda yer alan yard\u0131mc\u0131 ekran \u00fczerinde bulunan a deli\u011findeki bantlar\u0131n say\u0131s\u0131n\u0131 ifade eder.) yar\u0131\u00e7ap\u0131n\u0131 p ile g\u00f6sterelim {\u015fekil 6.2). Bellidir ki, j. band\u0131n alan\u0131, s\u0131ras\u0131yla; j ve j-1 numaral\u0131 bantlar\u0131n olu\u015fturduklar\u0131 y\u00fczeylerin alanlar\u0131 fark\u0131na e\u015fittir, j say\u0131da halka bantlar\u0131n\u0131 i\u00e7eren k\u00fcre y\u00fczeyi k\u0131sm\u0131n\u0131n y\u00fcksekli\u011fini hj ile g\u00f6sterelim (\u015fekil 6.2). K\u00fcre yar\u0131\u00e7ap\u0131 R oldu\u011funda, sj = 2pRhj olur.
\nYukar\u0131daki a\u00e7\u0131klamalar dikkate al\u0131n\u0131rsa,
\nDsj = sj – sj-1 = 2pR(hj \u2013 hj-1) (6.5)
\nyaz\u0131labilir, hj yi bulmak i\u00e7in SMjC ve MjCB \u00fc\u00e7genlerini dikkate alal\u0131m. \u015eeki6.2’den g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi : R2 \u2013 (R \u2013 hj)2 = rj2 \u2013 (r0 + hj)2 ve buradan, h = olur. \u00d6te yandan, rj = r0j oldu\u011fundan \u015feklinde bulunur. l << r0 ve l<
\nE0j = (6.8)
\n\u015feklinde ifade edilebilir. (6.8) ifadesi (6.4) ifadesini sadele\u015ftirmeye imk\u00e2n verir. Ger\u00e7ekten, (6.4) ifadesinde tek numaral\u0131 genlikler, kendilerinin yar\u0131lar\u0131 toplam\u0131 ile temsil edilirse;
\nE0 =
\n+ \u2026 + (6.9)
\nE0 =
\n+ (6.9a)
\nyaz\u0131labilir. (6.9) ve (6.9a) ifadeleri s\u0131ras\u0131yla j nin tek ve \u00e7ift de\u011ferlerine kar\u015f\u0131l\u0131k gelen ifadelerdir. (6.8) ifadesi (6.9) ve (6.9a) ifadelerinde nazara al\u0131n\u0131rsa parantez i\u00e7indeki ifadelerin s\u0131f\u0131ra e\u015fit oldu\u011fu g\u00f6r\u00fcl\u00fcr. B\u00f6ylece, (6.9) ve (6.9a) ifadeleri s\u0131ras\u0131yla a\u015fa\u011f\u0131daki ifadelere d\u00f6n\u00fc\u015f\u00fcrler.
\nE0 = (6.10)
\nE0 = (6.10a)
\nTekrar hat\u0131rlayal\u0131m ki, (6.10) ifadesi j nin tek, (6.10a) ifadesi ise \u00e7ift de\u011ferlerine uygun gelir.
\nGenlikler bant numaras\u0131n\u0131n artmas\u0131 ile k\u00fc\u00e7\u00fcld\u00fc\u011f\u00fcnden j nin 1 den yeterince b\u00fcy\u00fck de\u011ferlerinde E0j-1 = E0j al\u0131nabilir. Bu halde, (6.10a) ifadesi a\u015fa\u011f\u0131daki gibi yaz\u0131labilir.
\nE0 = (6.10b)
\n(6.10) ve (6.10b) ifadeleri genelle\u015ftirilirse,
\nE0 = (6.11)
\nolur. Burada (+) i\u015fareti j’nin tek ve (-) i\u015fareti ise \u00e7ift (j delikte yer alan Fresnel bantlar\u0131n\u0131n say\u0131s\u0131d\u0131r.) de\u011ferlerine uygundur.<\/p>\n","protected":false},"excerpt":{"rendered":"