Misalin Matsalar Rarraba Haske
Rarraba haske wani lamari ne da ke faruwa lokacin da raƙuman haske suka ratsa ta cikin wani kunkuntar buɗaɗɗiya ko kuma a kusa da wani cikas suka watse waje. Wannan lamari yana ba da shaida cewa haske yana da halayen raƙuman ruwa kuma muhimmin ra'ayi ne a fannin kimiyyar lissafi. A cikin wannan labarin, za mu tattauna misalan da aka saba gani na matsalolin rarraba haske, tare da tattaunawa da bayani.
Pendahuluan
Masanin kimiyya ɗan ƙasar Italiya Francesco Maria Grimaldi ne ya fara bayyana bambancin a ƙarni na 17. Bambanci yana faruwa ne lokacin da raƙuman haske suka canza alkiblarsu ta yaɗuwa yayin da suke ratsawa ta cikin wani buɗaɗɗe ko cikas. Wannan yana haifar da yanayin tsangwama na bambancin. Gabaɗaya, bambancin yana bayyana ne lokacin da tsawon hasken ya yi daidai da girman buɗewa ko cikas ɗin da yake ratsawa ta.
Ana iya bayanin abin da ke haifar da rarrabuwa ta amfani da samfura guda biyu na zahiri: Tsarin Wave da Tsarin Geometric Optical. Don ƙididdigewa da kuma hasashen tsarin rarrabuwar haske, yawanci ana amfani da lissafin rarrabuwar da Augustin-Jean Fresnel da Joseph von Fraunhofer suka ƙirƙira.
Asali na Ma'anar Diffraction
Kafin tattauna matsalolin misalai, yana da mahimmanci a fahimci wasu mahimman ra'ayoyi a cikin bambancin haske:
1. Rabe-rabe Guda Ɗaya da Biyu: Ana iya ganin tsarin rarraba haske mafi sauƙi lokacin da haske ya ratsa ta cikin rabe ɗaya ko biyu. Tsarin da ya biyo baya shine jerin rabe-raben haske da duhu akan allon lura.
2. Layukan Tsangwama: Layukan haske da duhu da ke kan allon sakamakon tsangwama ne tsakanin raƙuman haske da aka karkatar. Layukan haske ana kiransu layukan tsangwama masu gina jiki, yayin da layukan duhu sakamakon tsangwama ne masu lalata.
3. Tsawon Wave: Tsawon wave na hasken da aka yi amfani da shi yana tasiri sosai ga tsarin diffraction da aka samu. Haske mai tsawon wave zai samar da tsarin diffraction mai faɗi.
4. Kusurwar Diffraction: Ana iya tantance kusurwar da haske ke haskakawa ta amfani da ƙa'idodin trigonometry da kuma tsawon hasken da aka yi amfani da shi.
Misalin Matsalar Rarraba Haske
Bari mu tattauna wasu misalan matsalolin da aka saba fuskanta a cikin nazarin bambancin haske.
Misali Tambaya ta 1: Rarraba Rataye Guda Ɗaya
Tambaya: Hasken laser mai tsawon nisan nm 600 yana ratsawa ta cikin rami ɗaya mai faɗin mm 0,2. Lissafa kusurwar diffraction θ don tsari na farko (m=1).
Tattaunawa: Idan aka yi la'akari da bambancin rarrabuwar rata ɗaya, za mu iya amfani da lissafin rarrabuwa mai zuwa:
\[ a \sin \theta = m\lambda \]
Ina:
– \(a \) shine faɗin gibin,
– \( \theta \) shine kusurwar diffraction,
– \( \lambda \) shine tsawon haske,
– \( m \) shine tsarin rarrabawa.
An bayar:
– \( \lambda = 600 \) nm = \( sau 600 10^{-9} \) m,
– \( a = 0.2 \) mm = \( 0.2 \sau 10^{-3} \) m,
– \( m = 1 \).
Sauya dabi'u cikin lissafi,
\[ 0.2 \sau 10^{-3} \sin \theta = 1 \sau 600 \sau 10^{-9} \]
Magance matsalar \( \sin \theta \),
\[ \sin \theta = \frac{600 \sau 10^{-9}}{0.2 \sau 10^{-3}} \]
Lissafi \( \sin \theta \),
\[ \sin \theta = 0.003 \]
Amfani da kalkuleta don samun kusurwar \( \theta \),
digiri na \( \theta \kimanin 0.172 \).
Don haka, kusurwar diffraction na tsari na farko shine kimanin digiri 0.172.
Misali Tambaya ta 2: Rarraba Rataye Biyu
Tambaya: Haske mai tsawon nisan nm 500 yana ratsawa ta cikin rami mai nisan nisan da ke tsakanin ramukan 0,1 mm. Lissafa matsayin layin haske na biyu akan allon wanda yake da nisan mita 2 daga ramin.
Tattaunawa: Amfani da lissafin rarrabawar ramuka biyu:
\[d \sin \theta = m\lambda \]
Ina:
– \( d \) shine nisan da ke tsakanin gibin biyu,
– \( \lambda \) shine tsawon haske,
– \( m \) shine tsarin rarrabawa.
Domin nemo matsayin da ke kan allon (\( y \)) na \( \theta \), muna amfani da:
\[y = L \tan \theta \]
Ga ƙaramin \( \theta \), \( \tan \theta \approx \sin \theta \), da kuma \( L \) shine nisan allon daga tsaga.
An bayar:
– \( \lambda = 500 \sau 10^{-9} \) m,
– \( d = 0.1 \sau 10^{-3} \) m,
– \( L = 2 \) m,
– \( m = 2 \).
Sauya dabi'u cikin lissafi,
\[ 0.1 \sau 10^{-3} \sin \theta = 2 \sau 500 \sau 10^{-9} \]
Magance matsalar \( \sin \theta \),
\[ \sin \theta = \frac{1000 \sau 10^{-9}}{0.1 \sau 10^{-3}} \]
Lissafi \( \sin \theta \),
\[ \sin \theta = 0.01 \]
A ɗauka cewa \( \sin \theta = \tan \theta \) na nisan da ya yi yawa, sannan a maye gurbinsa da lissafin matsayi,
\[ y = sau 2 0.01 = 0.02 \] m ko 20 mm.
Don haka, matsayin layin haske na biyu akan allon yana da nisan mm 20 daga tsakiyar allon.
Penutup
Diffraction na haske batu ne da ke nuna cewa haske yana aiki kamar raƙuman ruwa. Wannan lamari yana ba da muhimman amfani a fannoni daban-daban na kimiyya, musamman na gani da kuma na gani. Fahimtar diffraction ba wai kawai ya dogara ne akan ka'ida ba, har ma ta hanyar warware matsaloli daban-daban na aiki waɗanda zasu iya taimakawa wajen zurfafa fahimtar halayen raƙuman haske.
Tare da ci gaban fasaha don lura da fahimtar halayen haske, ana ci gaba da amfani da abin da ke haifar da rarrabuwar kawuna a cikin sabbin abubuwan da aka gano da aikace-aikacen fasaha, daga na'urorin hangen nesa zuwa kayan aikin aunawa masu inganci. Saboda haka, nazarin rarrabuwar kawuna ba wai kawai yana da sha'awar ilimi ba ne, har ma yana da tasiri mai amfani ga rayuwar yau da kullun da ci gaban fasaha.
