Misalai 27 na tsangwama da rarraba haske - rabe-raben haske biyu
1. An haskaka ramuka biyu masu kunkuntar 0,5 mm a tsakaninsu da haske mai tsawon nisan nm 600. Lissafa ƙananan ƙimar kusurwa uku waɗanda (1) tsangwama mai gina jiki ke faruwa (b) tsangwama mai lalata.
Tattaunawa
Ƙananan kusurwoyi guda uku da tsangwama mai gina jiki ke faruwa:
Ƙananan kusurwoyi guda uku da tsangwama mai gina jiki ke faruwa:
2. Hasken monochromatic yana ratsawa ta cikin ramuka biyu masu ƙunci da layi ɗaya. Nisa tsakanin ramukan shine 0,6 mm. Nisa tsakanin allon da ramukan shine 60 cm. Tsarin tsangwama da ke faruwa akan allon layi ne mai haske da duhu wanda aka raba ta hanyar nisan iri ɗaya. Idan nisan da ke tsakanin layuka biyu masu haske da ke maƙwabtaka shine 0,2 mm, a tantance tsawon hasken da aka yi amfani da shi.
Tattaunawa
An san cewa:
d = 0,6 mm = 0,0006 m = 6 x 10-4 m
y = 0,2 mm = 0,0002 m = 2 x 10-4 m
l = 60 cm = 600 mm = 0,6 m
An tambaya: Wane tsawon haske ake amfani da shi?
Amsa:
3. An haska rami mai ninki biyu da haske mai tsawon nisan mita 560. An sanya allo a nisan mita 1 daga ramin. Idan nisan da ke tsakanin ramukan biyu ya kai mm 0,5, to nisan da ke tsakanin sandunan haske guda biyu da ke kusa da shi...
A. 1,00 mm
B. 1,12 mm
C. 1,40 mm
D. 1,60 mm
E. 2,00 mm
Tattaunawa:
An sani :
An tambaya :
Nisa tsakanin madaukai biyu masu haske (y)
Jawab :
Amsar da ta dace ita ce B.
4. Nisa tsakanin fitilun mota guda biyu shine 110 cm. Matsakaicin tsawon hasken da fitilun biyu ke fitarwa shine 600 nm. Idan mutum ne wanda diamitansa na ɗalibi ya kai 2 mm ya lura da fitilun biyu, matsakaicin nisa tsakanin motar da mutumin don hasken fitilun biyu har yanzu suna bayyana daban shine...
A. 450 m
B. 2500 m
C. mita 3000
D. 4000 m
E. 5000 m
Tattaunawa:
An sani :
D = 2 mm = 2 x 10-3 mita
Tsawon hasken = 600 nm = 600 x 10-9 mita
Nisa tsakanin fitilun mota guda biyu = 110 cm = mita 1,1
An tambaya :
Nisa tsakanin motar da mutumin da ke lura da fitilun biyu (l)?
Jawab :
Domin a ga haske biyu a matsayin abubuwa biyu daban-daban, kusurwar (theta) dole ne ta fi kusurwar mahimmanci, wadda ta cika lissafin:
Amsar da ta dace ita ce C.
5. Zane da ke ƙasa yana nuna gwajin Young. Idan d shine nisan da ke tsakanin ramukan biyu, L shine nisan da ke tsakanin tsagewar zuwa allon da kuma P2 shine nisan layin haske na 2 daga layin haske na tsakiya, sannan tsawon hasken da aka yi amfani da shi (1 Å = 10-10 m) shine…
A. 3.000 Å
B. 4.000 Å
C. 5.000 Å
D. 5.500 Å
E. 6.000 Å
Tattaunawa
An sani :
Nisa tsakanin ramuka biyu (d) = 1 mm = 1 x 10-3 mita
Nisa daga tsagi zuwa allo (L) = mita 1
Nisa tsakanin layin haske na 2 daga layin haske na tsakiya (P)2) = 1 mm = 1 x 10-3 mita
Umarni (n) = 2 (hasken tsakiya shine hasken farko don haka n = 0. Haske na biyu shine layin haske na farko don haka n = 1, n = layin haske na daƙiƙa 2)
An tambaya : Tsawon hasken (λ) da ake amfani da shi shine…
Jawab :
Tsarin tsatsagewa mai ratsawa biyu (tsatsagewa mai gina jiki) :
d sin θ = n λ
sin θ ≈ tan θ = P2 / L = (1 x 10-3) / 1 = 1 x 10-3 mita
Tsawon hasken raƙuman ruwa :
λ = d zunubi θ / n
λ = (1 x 10-3)(1 x 10-3) / 2 = (1 x 10-62
λ = 0,5 x 10-6 mita = 5 x 10-7 mita
λ = 5000 x 10-10 mita
λ = 5000 Å
Amsar da ta dace ita ce C.
6. A cikin wani gwaji tsangwama mai ragi biyu, bayanan da aka samu kamar yadda aka nuna a hoton da ke gefe. Don haka ƙimar tsawon tsayi da aka yi amfani da ita ita ce… (1 m = 1010 Å)
A. 4500 Å
B. 5000 Å
C. 6000 Å
D. 6500 Å
E. 7000 Å
Tattaunawa
An sani :
Nisa tsakanin ramuka biyu (d) = 0,8 mm = 8 x 10-4 mita
Nisa daga tsagi zuwa allo (L) = mita 1
Nisa daga layin haske na 4 daga layin haske na tsakiya (P) = 3 mm = 3 x 10-3 mita
Umarni (n) = 4
An tambaya : Tsawon hasken (λ) da ake amfani da shi shine…
Jawab :
Tsarin tsatsagewa mai ratsawa biyu (tsatsagewa mai gina jiki) :
d sin θ = n λ
sin θ ≈ tan θ = P / L = (3 x 10-3) / 1 = 3 x 10-3 mita
Tsawon hasken raƙuman ruwa :
λ = d zunubi θ / n
λ = (8 x 10-4)(3 x 10-3) / 4 = (24 x 10-74
λ = 6 x 10-7 mita = 6000 x 10-10 mita
λ = 6000 Å
Amsar da ta dace ita ce C.
7. Hoton da ke gefe zane ne na hanyar haskoki masu haske a cikin taron tsagawa mai katsewa biyu S.1 da kuma S2maki A da B layuka ne guda biyu masu duhu a jere kuma tsawon da aka yi amfani da shi shine 6000 Å (1 Å = 10)-10 m). Nisa tsakanin ramukan biyu shine…
A. 0,015 mm
B. 0,2 mm
C. 1,5 mm
D. 1,6 mm
E. 1,8 mm
Tattaunawa
Ana ƙididdige nisan da ke tsakanin ramukan biyu ta amfani da dabarar tsangwama mai gina jiki idan aka yi la'akari da cewa nisan da ke tsakanin layukan duhu guda biyu a jere iri ɗaya ne da nisan da ke tsakanin layukan haske guda biyu a jere.
An sani :
Nisa daga tsagi zuwa allo (L) = mita 1
Tsawon tsayin da aka yi amfani da shi (λ) = 6000 Å = 6000 x 10-10 mita = 6 x 10-7 mita
Nisa tsakanin layin haske na tsakiya zuwa layin haske na farko (P) = 0,2 mm = 0,2 x 10-3 mita = 2 x 10-4 mita
Tsarin layi mai haske na farko (n) = 1
An tambaya : Nisa tsakanin gibin biyu (d)
Jawab :
Tsarin tsangwama mai gina jiki :
d = n λ / zunubi θ
sin θ ≈ tan θ = P / L = (2 x 10-4) / 1 = 2 x 10-4 mita
Nisa tsakanin gibin biyu :
d = n λ / zunubi θ = (1) (6 x 10-7) / (2 x 10-4)
d = (6 x 10-7) / (2 x 10-4) = (3 x 10-3)
d = mita 0,003
d = 3 mm
8. Idan raƙuman haske guda biyu masu tsawon nisan nm 600 suka fuskanci tsangwama mai gina jiki, nawa ne hanyar raƙuman ruwan za ta bambanta?
Tattaunawa: Don tsangwama mai gina jiki, bambancin hanyoyin raƙuman ruwa dole ne ya zama nλ, inda n lamba ce. Idan n=0, to bambancin hanyoyin raƙuman ruwa shine 0 nm.
9. Raƙuman haske mai tsawon nisan nm 500 za a raba su ta cikin wani ɗan ƙaramin rami. Idan nisan da ke tsakanin ramin da allon mita 2 ne, kuma nisan da ke tsakanin tsakiyar tsarin rarrabawa da tsari na farko shine mm 5, nawa ne faɗin ramin?
Tattaunawa: Ta amfani da lissafin diffraction \( a\sin \theta = m\lambda \), inda \( a \) shine faɗin tsagewa, \( m \) shine tsari, kuma \( \theta \) shine kusurwa, zamu iya samun faɗin tsagewa: \( a = \frac{{m\lambda}}{{\sin \theta}} = \frac{{(1)(500 \times 10^{-9}\, \text{m})}}{{\sin \left( \frac{{5 \times 10^{-3}\, \text{m}}}{{2\, \text{m}}} \right)}} \approx 5 \times 10^{-4}\, \text{m} \).
10. Idan raƙuman haske guda biyu masu tsawon nisan nm 400 suka fuskanci tsangwama mai illa, nawa ne hanyar raƙuman ruwan za ta bambanta?
Tattaunawa: Don tsangwama mai lalatawa, bambancin hanyoyin raƙuman ruwa dole ne ya kasance \( (n + \frac{1}{2})\lambda \). Idan n=0, to bambancin hanyoyin raƙuman ruwa shine nm 200.
11. Me zai faru idan faɗin tsagewar a cikin gwajin diffraction ya fi tsawon haske girma?
Tattaunawa: Idan faɗin tsaga ya fi tsawon hasken girma, tsarin diffraction ɗin ba zai yi haske sosai ba kuma zai yi wahalar gani.
12. A cikin gwajin da Young ya yi na yankewa biyu tare da tsawon tsayin nm 650, an raba ramukan 0,1 mm da 0,2 mm. Menene tazara tsakanin madaurin duhu na farko da na biyu akan allo mai nisan mita 1?
Tattaunawa: Ana iya samun nisan da ke tsakanin madaurin duhu ta amfani da lissafin tsangwama \( y = \frac{{m\lambda D}}{{d}} \), inda \( m = 1 \) shine tsari na farko, \( D \) shine nisan da ke tsakanin allon, kuma \( d \) shine nisan da ke tsakanin madaurin duhu na farko da na biyu shine: \( y = \frac{{(1)(650 \times 10^{-9}\, \text{m})(1\, \text{m})}}{{0,1 \times 10^{-3}\, \text{m}}} – \frac{{(0)(650 \times 10^{-9}\, \text{m})(1\, \text{m})}}{{0,1 \times 10^{-3}\, \text{m}}} \approx 6,5\, \text{mm} \).
13. Idan haske mai tsawon nisan nm 700 ya bugi rami biyu tare da nisan mm 0,3 tsakanin ramukan, menene nisan da ke tsakanin madaurin haske na farko da na biyu akan allo mai nisan mita 1,5?
**Tattaunawa**: Ta amfani da irin wannan lissafi ga tambaya ta 5, za mu iya samun nisan da ke tsakanin madauri masu haske na farko da na biyu shine: \( y \approx 7\, \text{mm} \).
13. Menene tsangwama mai gina jiki kuma ta yaya yake faruwa?
Tattaunawa: Tsangwama mai gina jiki tana faruwa ne lokacin da raƙuman haske guda biyu suka haɗu kuma bambancin hanyarsu shine ninki na raƙuman ruwa (nλ). Wannan yana haifar da ƙaruwar girman raƙuman ruwa.
14. Menene tsangwama mai lalatawa kuma ta yaya take faruwa?
Tattaunawa: Tsangwama mai lalata yana faruwa ne lokacin da raƙuman haske guda biyu suka haɗu kuma bambancin hanyarsu shine sau ɗaya mai ban mamaki na rabin raƙuman raƙuman ruwa \((n + \frac{1}{2})\lambda\). Wannan yana haifar da raguwa ko raguwar girman raƙuman ruwa.
15. A cikin rarrabawa ta hanyar rabawa guda ɗaya, me zai faru da tsarin rarrabawa idan an rage faɗin rabawa?
Tattaunawa: Idan aka rage faɗin tsaga, tsarin diffraction zai yi faɗi, kuma za a raba madaurin haske da duhu.
16. Me zai faru da tsarin tsangwama a cikin gwajin yankewa biyu idan an ƙara tazara tsakanin yankewar?
Tattaunawa: Idan aka ƙara tazara tsakanin ramukan, tsarin tsangwama zai yi kauri sosai, kuma tazara tsakanin sandunan haske da duhu zai ragu.
17. A cikin gwajin da Young ya yi na raba rami biyu tare da tsawon tsayin nm 550 da kuma ramin 0,15 mm, menene tazara tsakanin madaukai masu haske na biyar da na 10 a kan allo mai nisan mita 2?
Tattaunawa: Ta amfani da lissafi makamancin haka da matsala ta 5, za mu iya gano nisan da ke tsakanin madaukai masu haske na biyar da na 10 shine: \( y \approx 36,67\, \text{mm} \).
18. Ta yaya tsawon tsayi ke shafar tsarin diffraction?
Tattaunawa: Girman tsawon raƙuman ruwa zai haifar da tsarin diffraction mai faɗi, yayin da ƙaramin tsawon raƙuman ruwa zai haifar da tsarin diffraction mai kunkuntar.
19. Idan haske mai tsawon nisan nm 450 ya bugi rami biyu tare da nisan mm 0,25 tsakanin ramukan, menene nisan da ke tsakanin madaurin duhu na farko da na biyu akan allo mai nisan mita 1?
Tattaunawa: Ta amfani da irin wannan lissafi ga tambaya ta 5, za mu iya gano nisan da ke tsakanin madaurin duhu na farko da na biyu shine: \( y \approx 1,8\, \text{mm} \).
20. Ta yaya za a tantance matsayin madaurin mai haske a cikin tsarin tsangwama mai rabe biyu?
Tattaunawa: Ana iya tantance matsayin madaurin haske a cikin tsarin tsangwama mai rabe biyu ta amfani da lissafin \( y = \frac{{m\lambda D}}{{d}} \), inda \( m \) shine tsari, \( \lambda \) shine tsawon tsayi, \( D \) shine nisa zuwa allon, kuma \( d \) shine nisa tsakanin tsagewar.
21. Ta yaya za a tantance matsayin madaurin duhu a cikin tsarin rarrabawa mai ragi ɗaya?
Tattaunawa: Ana iya tantance matsayin madaurin duhu a cikin tsarin rarrabawa mai tsaga ɗaya ta amfani da lissafin \( a\sin \theta = m\lambda \), inda \( a \) shine faɗin tsaga, \( m \) shine tsari, kuma \( \theta \) shine kusurwa.
22. Me zai faru da tsarin tsangwama idan aka maye gurbin tushen haske da gajeren zango?
Tattaunawa: Idan tsawon tsayin ya yi gajere, tsarin tsangwama zai yi yawa, kuma za a rage tazara tsakanin madaurin haske da duhu.
23. Ta yaya gwajin da aka yi wa rami biyu yake aiki don nuna yanayin raƙuman haske?
Tattaunawa: Gwajin da aka yi ta hanyar raba haske sau biyu yana nuna yanayin raƙuman haske ta hanyar samar da tsarin tsangwama mai haske da duhu a kan allo. Wannan tsari ya samo asali ne ta hanyar haɗa raƙuman ruwa daga ramukan biyu, wanda ke nuna yanayin raƙuman haske.
24. Bayyana bambanci tsakanin tsangwama da rarrabuwa.
Tattaunawa: Tsangwama tana da alaƙa da haɗuwar raƙuman ruwa biyu ko fiye waɗanda ke haifar da ƙaruwa ko raguwa a girmansu, yayin da rarrabuwar ra'ayi ke da alaƙa da lanƙwasa raƙuman ruwa yayin da suke wucewa ta cikin wani buɗaɗɗe ko kewaye da wani abu.
25. A cikin gwajin da Young ya yi na raba biyu, bayyana dalilin da yasa alamu masu duhu da haske suka bayyana akan allon.
Tattaunawa: Tsarin duhu da haske suna bayyana ne saboda tsangwama mai gina jiki da lalatawa tsakanin raƙuman ruwa daga ramukan biyu. Tsarin haske yana bayyana ne lokacin da tsangwama mai gina jiki ta faru (bambancin hanya shine yawan tsayin tsayi), kuma tsarin duhu yana bayyana lokacin da tsangwama mai lalata ta faru (bambancin hanya shine yawan tsayin rabin tsayin tsayi).
25. Ta yaya tsarin rarrabawa na tsaga ɗaya ya bambanta da na tsaga biyu?
Tattaunawa: Tsarin rarrabawa na tsaga ɗaya ya ƙunshi tsakiyar madauri mai haske tare da madauri masu duhu da haske a jere a kowane gefe. A cikin tsaga biyu, akwai ƙarin tsarin tsangwama wanda hulɗar raƙuman ruwa daga tsaga biyu ke haifarwa, wanda hakan ya sa tsarin ya fi rikitarwa.
Tsangwama Mai Sauƙi
Shisshigi wani abu ne na zahiri da ke faruwa lokacin da raƙuman haske biyu ko fiye suka haɗu suka haɗu. Wannan yana haifar da sabon tsari tare da girman da zai iya zama mafi girma ko ƙasa da girman raƙuman ruwa na asali.
Tsangwama Mai Ginawa
Tsangwama mai gina jiki yana faruwa ne lokacin da bambancin hanyar raƙuman ruwa ya kasance mai yawa na tsawon raƙuman ruwa (nλ), wanda ke haifar da ƙaruwar girman raƙuman ruwa. Wannan tsari yana bayyana a matsayin madaukai masu haske akan allon a cikin gwaje-gwaje kamar su Young's double-slit.
Tsangwama Mai Lalacewa
Tsangwama mai lalata yana faruwa ne lokacin da bambancin hanyar raƙuman ruwa ya kasance mai yawa na rabin raƙuman ruwa . Wannan yana haifar da raguwa ko raguwar girman raƙuman ruwa, wanda ake gani a matsayin wani yanki mai duhu a cikin tsarin tsangwama.
Diffraction na Haske
Diffraction wani lamari ne da ke faruwa lokacin da raƙuman haske suka ratsa ta cikin wani kunkuntar buɗewa ko kuma a kusa da wani abu. Wannan yana sa raƙuman hasken su lanƙwasa su bazu, suna samar da tsarin diffraction na musamman.
Diffraction ta hanyar Ragewa Guda ɗaya
A cikin tsagi ɗaya, tsagi yana samar da tsari mai haske na tsakiya tare da madauri masu duhu da haske a jere a kowane gefe. Faɗin tsagi yana daidai da faɗin tsarin tsagi.
Diffraction ta hanyar Rage Biyu
A cikin ramin da aka raba biyu, diffraction yana samar da tsari mai rikitarwa. Baya ga tsarin diffraction daga kowace rami, akwai kuma tsarin tsangwama da ke haifar da hulɗar raƙuman ruwa daga ramukan biyu.
Gwaje-gwaje Masu Muhimmanci
Gwajin Rage Rage Biyu na Young
Gwajin Thomas Young mai sassauta biyu hanya ce ɗaya ta lura da tsangwama da rarrabuwar haske. Haske da yanayin duhu da ke kan allon suna nuna yanayin raƙuman haske, suna goyon bayan ka'idar raƙuman haske.
Kammalawa
Tsangwama da rarrabuwar haske abubuwa ne da ke nuna yanayin raƙuman haske. Fahimtar yadda tsangwama da rarrabuwar haske ke aiki yana ba mu damar fahimtar halaye da halayen haske, waɗanda ke da amfani mai mahimmanci a fannoni kamar na gani, fasahar sadarwa, da magani.
Nazarin tsangwama da rarrabuwar kawuna yana taimakawa wajen haɓaka fasahohi kamar na'urorin microscopes, na'urorin hangen nesa, da sauran kayan aikin gani, waɗanda suka dogara da tsarin tsangwama da rarrabuwa don inganta ƙuduri da inganci.
