Muenzaniso weDambudziko reKupindira kweChiedza
Kupindirana kwechiedza chiitiko chepanyama chinoitika kana mafungu maviri kana anopfuura echiedza akasangana uye achibatana, zvichikonzera maitiro akasiyana ekupararira kwesimba rechiedza. Chiitiko ichi chakabatana zvakanyanya nehunhu hwemafungu echiedza uye chinoshanda sehumbowo hwakakosha hwedzidziso yemafungu echiedza. Chinyorwa chino chichaongorora pfungwa huru yekupindirana kwechiedza uye kupa mienzaniso yakati wandei yezvinetso uye mhinduro dzacho kuti tinzwisise zvakanyanya chiitiko ichi.
Pfungwa Yekutanga Yekupindirana Kwechiedza
Kupindirana kwechiedza kunoitika kana manyuko maviri kana anopfuura echiedza akabatana (manyuko ane urefu hwewavelength hwakafanana uye musiyano wechikamu unogara uripo) akasangana. Muchokwadi, kupindirana kunogona kuva nekuvaka kana kuparadza. Kupindirana kunovaka kunoitika kana mafungu asangana muchikamu chimwe chete, zvichikonzera amplitude yakakura. Kusiyana neizvi, kupindirana kunoparadza kunoitika kana mafungu asangana muzvikamu zvakasiyana, achibvisana uye zvichikonzera amplitude diki kana kuti zero.
Imwe ongororo yakakurumbira inoratidza kupindirana kwechiedza ndeyekuyedza kwaYoung kwekucheka kaviri. Mukuyedza uku, chiedza chinopfuudzwa nepakati pemipata miviri yakamanikana iri pedyo, zvichigadzira patani yekupindirana pachidzitiro chiri kumashure kwemipata. Patani iyi inoratidza mitsetse yakatevedzana yakajeka neyakasviba, ichiratidza kupindirana kunovaka uye kunoparadza.
Fomura Yekupindira Kwepakutanga
Kuti unzwisise kupindira, zvakakosha kuti uve nehunyanzvi hwekutanga hunoshanda kune chiitiko ichi. Chaizvoizvo, nzvimbo dzakajeka (kupindira kwekuvaka) uye dzakasviba (kupindira kwekuparadza) mukuyedza kwe double-slit dzinogona kutsanangurwa ne equation inotevera:
1. Kupindira Kunovaka:
\[
d \sin \theta = m \lambda
\]
Di mana:
– \( d \) ndiyo daro riri pakati pemipata miviri.
– \( \theta \) ndiyo kona inoenda kumutsetse wakajairika apo simba guru rinoitika.
– \( m \) inhamba yakakwana (0, 1, 2, …).
– \( \lambda \) ndiyo hupamhi hwechiedza.
2. Kupindira Kunoparadza:
\[
d \sin \theta = \left(m + \frac{1}{2}\right) \lambda
\]
Muenzaniso weDambudziko reKupindira kweChiedza
Kuti tishandise pfungwa yekupindira, heino mimwe mienzaniso yemibvunzo nehurukuro dzayo:
Muenzaniso Mubvunzo 1
Mubvunzo:
Mwaranzi wechiedza une urefu hwemafungu e600 nm unopfuura nepakati pemipata miviri yakaparadzana ne 0,1 mm. Kana chidzitiro chikaiswa mamita maviri kumashure kwemipata, sarudza daro riri pakati pemitsetse yekutanga yakajeka muchimiro chekupindira.
Kukurukurirana:
Kuti tiwane daro riri pakati pemitsara yekutanga yakajeka, tinogona kushandisa fomura yekubatanidza inovaka:
\[
d \sin \theta = m \lambda
\]
Pano tiri kutsvaga daro riri pachikirini rakaenzana nekona \( \theta \). Kune makona madiki, tinogona kushandisa approximation:
\[
\sin \theta \approx \tan \theta = \frac{x}{L}
\]
Apo \( x \) iri daro riri pakati pemitsetse yakajeka pachiratidziro uye \( L \) iri daro riri pakati pemitsetse nechidzitiro. Muchiitiko ichi, \( m = 1 \) yemutsetse wekutanga wakajeka kuitira kuti:
\[
d \frac{x}{L} = \lambda
\]
Saka:
\[
x = \frac{\lambda L}{d}
\]
Tichitsiva tsika dzinozivikanwa, tinowana:
\[
x = \frac{600 \nguva 10^{-9} \, \text{m} \nguva 2}{0,1 \nguva 10^{-3} \, \text{m}} = 0,012 \, \text{m} = 12 \, \text{mm}
\]
Saka, daro riri pakati pemitsetse yekutanga yakajeka i12 mm.
Muenzaniso Mubvunzo 2
Mubvunzo:
Mukuyedza kwe "double-slit", mwenje miviri ine marefu akasiyana ewavelength inoshandiswa: 500 nm uye 600 nm. Kana daro riri pakati pemaburi iri 0,2 mm uye daro rekuenda kuchiratidziro riri 1,5 metres, sarudza nzvimbo yemutsara wechipiri wakajeka wewavelength yega yega.
Kukurukurirana:
Kuti tizive nzvimbo yemutsara wechipiri wakajeka (\( m = 2 \)) pahurefu hwewavelength yega yega, tinoshandisa equation:
\[
x = \frac{m \lambda L}{d}
\]
1. Pakureba kwehurefu hwe500 nm:
\[
x_1 = \frac{2 \nguva 500 \nguva 10^{-9} \, \text{m} \nguva 1,5 \, \text{m}}{0,2 \nguva 10^{-3} \, \text{m}} = 7,5 \, \text{mm}
\]
2. Pakureba kwehurefu hwe600 nm:
\[
x_2 = \frac{2 \nguva 600 \nguva 10^{-9} \, \text{m} \nguva 1,5 \, \text{m}}{0,2 \nguva 10^{-3} \, \text{m}} = 9 \, \text{mm}
\]
Saka, nzvimbo yemutsara wechipiri wakajeka wehurefu hwe500 nm iri 7,5 mm kubva pakati, nepo ye600 nm iri 9 mm.
Mhedziso
Chiitiko chekupindirana kwechiedza chinosimbisa hunhu hwemafungu echiedza. Nekunzwisisa nekushandisa mafomura ane chekuita nekupindirana, tinogona kuona zvinhu zvakasiyana-siyana zvemaitiro ekupindirana, zvakaita senzvimbo uye daro riri pakati pemitsetse yakajeka nerima. Chinyorwa chino chinopa kunzwisisa kwekutanga kwekupindirana kwechiedza uye chinokurudzira vaverengi kuti vabatanidzwe mukuongorora nekugadzirisa matambudziko ane chekuita nechiitiko ichi chinonakidza. Kudzidza kwakawanda kwekupindirana kwechiedza kunogona kusanganisira kuyedza nekuverenga pasi pemamiriro ezvinhu akaomarara kuti tiwedzere ruzivo rwedu rwe optics ne physics yemafungu.
