11 mau laʻana o nā nalu māmā
E hoʻolohe i nā ʻōlelo aʻe:
(1) E hoʻololi i ka grid me kahi grid me ka nui o nā laina no ka millimeter.
(2) Mālamalama e hāʻule ana mai ka uliuli a i ka melemele
(3) E hoʻololi i ke kukui i hoʻopuka ʻia mai ka ʻulaʻula a i ka ʻōmaʻomaʻo
(4) E hoʻoneʻe i ka pale a kokoke i ka grid
ʻO ka mea i hoʻokomo ʻia i ka hoʻoikaika ʻana e hoʻonui i ka laulā o ke kāʻei ʻālohilohi i ka hoʻokolohua diffraction grating ʻo ia...
Pahana
ʻO ke ʻano hoʻopilikia pālua (hoʻopilikia kūkulu):
He liʻiliʻi loa ka laulā o ka ʻoki (d) i hoʻohālikelike ʻia me ka mamao ma waena o ka ʻoki a me ka pale (L) no laila he liʻiliʻi loa ke kihi. He liʻiliʻi loa ke kihi i hiki ai i ka waiwai o ka hewa θ tangent e hoʻokokoke ana θ.
sin θ ≈ tan θ = y / L
ʻIkepili:
y = ka laulā o ke kāʻei ʻālohilohi, n = ke kauoha, λ = ka nalu, L = ka mamao ma waena o ke grating a me ka pale, d = ka laulā o ka ʻoki.
d = 1 / (4000 laina / kenimika) = 0,00025 kenimika
(1) E hoʻololi i ka grid me kahi grid me ka nui o nā laina no ka millimeter.
laʻana:
d = 1 / (1000 laina / kenimika) = 0,001 kenimika
d = 1 / (2000 laina / kenimika) = 0,0005 kenimika
d = 1 / (3000 laina / kenimika) = 0,0003 kenimika
d = 1 / (4000 laina / kenimika) = 0,00025 kenimika
Ma muli o kēia helu ʻana, inā ʻoi aku ka nui o nā laina no ka milimita, a laila ʻoi aku ka liʻiliʻi o ka laulā o ka ʻoki (d). Ma muli o ke ʻano ma luna, inā ʻoi aku ka liʻiliʻi o ka laulā o ka ʻoki (d), a laila ʻoi aku ka nui o ka laulā o ke kāʻei ʻālohilohi (y).
He ʻoiaʻiʻo kēia ʻōlelo.
(2) Mālamalama e hāʻule ana mai ka uliuli a i ka melemele
ʻOi aku ka alapine (frequency) o ke kukui polū ma mua o ke kukui melemele, ʻo ka ʻaoʻao ʻē aʻe
ʻOi aku ka liʻiliʻi o ka nalu o ke kukui polū ma mua o ke kukui melemele.
Inā hoʻokuʻu ʻia ke kukui mai ka polū a i ka melemele, a laila e nui aʻe ka nalu.
Ma muli o ke ʻano ma luna, inā ʻoi aku ka nui o ka nalu, ʻoi aku ka nui o ka laulā o ke kāʻei ʻālohilohi (y).
He ʻoiaʻiʻo kēia ʻōlelo.
(3) E hoʻololi i ke kukui i hoʻopuka ʻia mai ka ʻulaʻula a i ka ʻōmaʻomaʻo
ʻOi aku ka haʻahaʻa o ke alapine (frequency) o ke kukui ʻulaʻula ma mua o ke kukui ʻōmaʻomaʻo, a ʻo ka ʻaoʻao ʻē aʻe
ʻOi aku ka lōʻihi o ka nalu o ke kukui ʻulaʻula ma mua o ke kukui melemele.
Inā hoʻokuʻu ʻia ke kukui mai ka ʻulaʻula a i ka ʻōmaʻomaʻo, a laila e liʻiliʻi ka nalu.
Ma muli o ke ʻano ma luna, inā ʻoi aku ka liʻiliʻi o ka nalu, ʻoi aku ka liʻiliʻi o ka laulā o ke kāʻei ʻālohilohi (y).
Ua hewa kēia ʻōlelo.
(4) E hoʻoneʻe i ka pale a kokoke i ka grid
ʻO ka hoʻoneʻe ʻana i ka pale a kokoke i ka grid ʻo ia hoʻi ka hōʻemi ʻana iā L. Ma muli o ke ʻano ma luna, inā ʻoi aku ka liʻiliʻi o ka mamao ma waena o ka grid a me ka pale (L), ʻoi aku ka liʻiliʻi o ka laulā o ke kāʻei ʻālohilohi (y).
Ua hewa kēia ʻōlelo.
2. Ka hoʻokahe ʻana o ke kukui
Ma kahi hoʻokolohua diffraction māmā e hoʻohana ana i kahi grating line.cm 4.500-1, ma luna o kahi pale i kau ʻia ma kahi mamao L mai ke grating, ʻike ʻia ka mamao o ke kaula ʻālohilohi o ke kauoha ʻelua he 1 mm. Inā pani ʻia ka grating i hoʻohana ʻia me kahi grating ʻē aʻe nona nā laina 5.400.cm-1, a laila ʻo ka mamao o ke kāʻei ʻālohilohi ʻelua i ana ʻia mai ke kāʻei ʻālohilohi waena he…
A. 0,6 mm
B. 0,9 mm
C. 1,2 mm
D. 1,6 mm
E. 2,2 mm
Pahana
Ua ʻike ʻia:
d1 = 1 / (4500 laina / kenimika) = 1/4500 kenimika
n1 = 2
y1 = 1 mm = 0,1 kenimika
d2 = 1 / (5400 laina / kenimika) = 1/ 5400 kenimika
n2 = 2
Ua nīnau ʻia: y2
Pane:
ʻO ke ʻano hoʻopilikia pālua (hoʻopilikia kūkulu):
hewa d θ = n λ
He ʻuʻuku loa ka laulā o ka ʻoki i hoʻohālikelike ʻia me ka mamao ma waena o ka ʻoki a me ka pale no laila he ʻuʻuku loa ke kihi. He ʻuʻuku loa ke kihi a kokoke ka waiwai o sin theta i ka tangent theta.
sin θ ≈ tan θ = y / L
hewa d θ = n λ
lā (y / L) = n λ
dy = n λ L
ʻIkepili:
d = ka laulā o ka ʻoki, y = ka mamao ma waena o ke kukui waena a me ke kukui kauoha nth, n = ke kauoha, λ = ka nalu, L = ka mamao ma waena o ke grating a me ka pale.
Hoʻokolohua 1:
d1 y1 =n1 λ L
(1/4500)(0,1) = (2) λ L
0,1 / 4500 = (2) λ L
0,1 / (2)(4500) = λ L
0,1 / 9000 = λ L
Hoʻokolohua 2:
d2 y2 =n2 λ L
(1/5400)(y2) = (2) λ L
y2 / 5400 = (2) λ L
y2 / (2)(5400) = λ L
y2 / 10.800 = λ L
Ua like ka nalu o ke kukui (λ) i hoʻohana ʻia a ua like nō hoʻi ka mamao ma waena o ke grating a me ka pale (L).
λ L = λ L
0,1 / 9000 = y2 / 10.800
(0,1)(10.800) = (y2)(9000)
1080 = y2 (9000)
y2 = 1080/9000
y2 = 0,12 knm
y2 = 1,2 mm
ʻO C ka pane pololei.
Ka Hoʻopilikia ʻana o ka Mālamalama
3. ʻElua mau ʻāpana haiki, he 2 mm ke kaʻawale, ua hoʻomālamalama ʻia ma ke ʻano kū pololei. Ma kahi pale he 1 mika mai nā ʻāpana, ua hoʻokumu ʻia kahi laina ʻālohilohi ʻehā, aia he 1 mm mai ka laina ʻālohilohi waena. ʻO ka nalu o ke kukui i hoʻohana ʻia…
A. 24 x 10-6 m
B. 8,0 x 10-6 m
C. 3,7 x 10-6 m
D. 2,0 x 10-6 m
E. 0,5 x 10-6 m
Pahana
Ua ʻike ʻia:
Ka mamao ma waena o nā ʻoki (d) = 2 mm = 2 x 10-3 mika
Kauoha (n) = 4
Ka mamao ma waena o ka pale a me ke kaawale (l) = 1 mika
Ka mamao Ka laina ʻālohilohi 4 mai ke kukui waena (y) = 1 mm = 1 x 10-3 mika = 10-3 mika
Ua nīnau ʻia: Ka lōʻihi o ka nalu o ke kukui (λ)
Pane:
ʻO ke ʻano hoʻopilikia pālua (hoʻopilikia kūkulu):
hewa d θ = n λ
ʻOi aku ka liʻiliʻi o ka mamao ma waena o nā ʻoki ma mua o ka mamao ma waena o nā ʻoki a me ka pale no laila he liʻiliʻi loa ke kihi. He liʻiliʻi loa ke kihi no laila ʻo ke kumukūʻai hewa θ hoʻokokoke ʻana tangen θ.
Ka lōʻihi o ka nalu o ke kukui (λ):
ʻO ka pane pololei ʻo E.
4. Ma ka hoʻokolohua a Young, ua hoʻohana ʻia ʻelua mau ʻāpana haiki, 3 mm ke kaʻawale kēlā me kēia, a ua kau ʻia kahi pale 1 m mai nā ʻāpana. Inā ua hana ʻia ke kukui ʻeono ma kahi mamao o 1 mm mai ke kukui waena, a laila ʻo ka nalu o ke kukui i hoʻohana ʻia...
A. 0,5 x 10-6 m
B. 2,0 x 10-6 m
C. 3,7 x 10-6 m
D. 8,0 x 10-6 m
E. 24 x 10-6 m
Pahana
Ua ʻike ʻia:
Ka mamao ma waena o nā ʻoki (d) = 3 mm = 3 x 10-3 mika
Kauoha (n) = 6
Ka mamao ma waena o ka pale a me ke kaawale (l) = 1 mika
Ka mamao Ka laina ʻālohilohi 6 mai ke kukui waena (y) = 1 mm = 1 x 10-3 mika = 10-3 mika
Ua nīnau ʻia: Ka lōʻihi o ka nalu o ke kukui (λ)
Pane:
Ka lōʻihi o ka nalu o ke kukui (λ):
ʻO A ka pane pololei.
Nā ʻano o nā nalu māmā
5. Nā ʻano o nā nalu:
(1) ʻano nalu lōʻihi
(2) hiki ke hoʻohuli i ke alapine (refract)
(3) hiki ke hoʻopilikia
(4) hiki ke hoʻopili ʻia
(5) koi ʻia kahi mea waena no kona hoʻolaha ʻana
ʻO ka ʻōlelo ma luna nei he ʻano o nā nalu māmā, ʻo ia ka helu…
A. (1), (2) a me (3)
B. (1), (2) a me (4)
C. (1), (3) a me (5)
D. (2), (3) a me (4)
E. (2), (2) a me (5)
Pahana
ʻO D ka pane pololei.
6. Nīnau Hoʻokolohua Lahui SMA/MA Physics 2015/2016 Helu 29
E hoʻolohe i ka ʻōlelo aʻe!
(1) Hiki ke hoʻopilikia
(2) Ke ʻike nei i ka polarization
(3) Ke ʻike nei i ka diffraction
(4) Ke kolo nei me ka ʻole o kahi waena
(5) Hiki ke hōʻike ʻia
ʻO ka ʻōlelo pololei ma luna e pili ana i nā ʻano o nā nalu kani ʻo ia ...
A. (1), (2), a me (3)
B. (1), (3), a me (5)
C. (1), (4), a me (5)
D. (2), (3), a me (4)
E. (3), (4), a me (5)
Pahana
(2) ʻIke ʻia ka polarization e nā nalu transverse. He mau nalu longitudinal nā nalu kani.
(4) ʻO nā nalu e laha ana me ka ʻole o kahi medium he mau nalu electromagnetic wale nō, ʻo nā nalu kani he mau nalu mechanical e pono ai kahi medium e laha.
ʻO ka pane pololei ʻo B.
ʻO ka Diffraction Grating
7. He 4.000 mau laina no kenimika o kahi grating diffraction. Hoʻomālamalama ʻia ke kukui monochromatic ma luna o ka grating, e hana ana i kahi laina ʻālohilohi lua-papa. Inā he 30° ke kihi o ka deviation,o, a laila ʻo ka nalu o ke kukui he… (1 Å = 10-10 m)
A. 8.000 Å
B. 6.250 Å
C. 5.000 Å
D. 4.500 Å
E. 4.000 Å
Pahana
Ua ʻike ʻia:
Paʻa o ka Lattice (d) = 1 / (4000 laina / kenimika) = 0,00025 kenimika = 2,5 x 10-4 kenimika = 2,5 x 10-6 mika
Kauoha (n) = 2
hewa 30o = 0,5
1 Å = 10-10 m
Ua nīnau ʻia: Ka lōʻihi o ka nalu o ke kukui (λ)
Pane:
ʻO ka pane pololei ʻo B.
8. He kukuna o ke kukui monochromatic me ka nalu o 2,5.10-7 m ma kahi grid i loaʻa he 10.000 mau hahau/cm. He aha ke kihi no kahi laina ʻālohilohi o ke kauoha ʻelua?
H. 30o
B. 37o
C. 45o
D. 53o
E. 60o
Pahana
Ua ʻike ʻia:
Paʻa o ka Lattice (d) = 1 / (10.000 laina / kenimika) = 0,0001 kenimika = 1 x 10-4 kenimika = 1 x 10-6 mika
Kauoha (n) = 2
Ka lōʻihi o ka nalu o ke kukui (λ) = 2,5 x 10-7 mika
Ua nīnau ʻia: Kihi (θ)
Pane:
ʻO A ka pane pololei.
9. Ke komo ʻana o ka ʻoki pālua
Ua hāʻule kahi kukuna o ke kukui melemele ma luna o ʻelua mau ʻāpana, e hana ana i kahi keakea ʻike ʻia ma ka pale. Mai ka ʻōlelo aʻe:
(1) E ʻoi aku ka laulā o ke kaula ʻālohilohi inā pani ʻia ke kukui melemele e ka uliuli
(2) E ʻoi aku ka laulā o ke kāʻei ʻālohilohi inā e hoʻemi ʻia ka mamao ma waena o nā ʻoki.
(3) ʻO ka mamao aku mai ke kukui waena, ʻo ka liʻiliʻi o ka ikaika.
(4) ʻo ka mamao aku mai ke kukui waena e mau ana ka ikaika.
ʻO ka ʻōlelo kūpono…
A. (1), (3) a me (4)
B. (1) a me (3) wale nō
C. (1) a me (4) wale nō
D. (2) a me (3) wale nō
E. (2) a me (4) wale nō
Pahana
ʻOi aku ka liʻiliʻi o ka mamao ma waena o nā ʻoki ma mua o ka mamao ma waena o nā ʻoki a me ka pale no laila he liʻiliʻi loa ke kihi. He liʻiliʻi loa ke kihi no laila ʻo ke kumukūʻai hewa θ hoʻokokoke ʻana tangen θ.
ʻO ke ʻano hoʻopilikia pālua (hoʻopilikia kūkulu)
ʻIkepili:
d = ka mamao ma waena o nā ʻoki, y = jʻalekohola laina ʻālohilohi i n mai ke kukui waena, l = ka mamao ma waena o ka pale a me ka ʻoki, n = ke kauoha, λ = pka nalu o ke kukui.
(1) E ʻoi aku ka laulā o ke kaula ʻālohilohi inā pani ʻia ke kukui melemele e ka uliuli
Ma muli o kēia haʻilula, ua like ka nui o nā laina ʻālohilohi (n) me ka lōʻihi gnā nalu (λ). Inā ʻoi aku ka liʻiliʻi o ka nalu, piʻi ka helu o nā laina ʻālohilohi (n). ʻOi aku ka lōʻihi o ka nalu o ke kukui melemele (alapine haʻahaʻa) ma mua o ke kukui polū. Inā pani ʻia ke kukui melemele me ka polū, lilo ka nalu i pōkole, no laila e piʻi ana ka helu o nā laina ʻālohilohi (n).
He ʻoiaʻiʻo kēia ʻōlelo.
(2) E ʻoi aku ka laulā o ke kāʻei ʻālohilohi inā e hoʻemi ʻia ka mamao ma waena o nā ʻoki.
Ma muli o ke ʻano hana ma luna, ua kūlike pololei ka mamao ma waena o nā ʻoki (d) me ka helu o nā laina ʻālohilohi (n). Inā hoʻemi ʻia ka mamao ma waena o nā ʻoki, e emi ana ka helu o nā laina ʻālohilohi (n).
Ua hewa kēia ʻōlelo.
(3) ʻO ka mamao aku mai ke kukui waena, ʻo ka liʻiliʻi o ka ikaika.
Pili ka ikaika i ka pae o ka ʻōlinolino. He kūlike ʻole ka ikaika me ka mamao; ʻo ka nui o ka mamao, ʻo ka haʻahaʻa o ka ikaika (ʻo ka emi ʻana o ke kukui).
He ʻoiaʻiʻo kēia ʻōlelo.
(4) ʻO ka mamao aku mai ke kukui waena, e mau ana ka ikaika.
Ua hewa kēia ʻōlelo.
ʻO ka pane pololei ʻo B.
10. He kukuna o ke kukui monochromatic me ka nalu o 5.10-7 Ua kuhikuhi ʻia ʻo m i ka grating. Inā he 2 m ka mamao ma waena o ka pale a me ka grating a puka mai kahi kukui ʻekolu ma ka pale ma kahi mamao o 150 cm mai ke kukui waena, a laila ʻo ka mamao ma waena o nā ʻoki he….
- 4.10-6 m
- 3.10-6 m
- 2.10-6 m
- 3.10-7 m
- 2.10-7 m
Pahana
Ua ʻike ʻia:
Ka lōʻihi o ka nalu (λ) = 5 x 10-7 mika
l = 2 mika
n = 3
y = 150 kenimika = 1,5 mika
Ua nīnau ʻia: paʻa mau o ka lattice
Pane:
hewa θ ≈ tan θ = y / l = 1,5 / 2 = 0,75 = 75 x 10-2
Ka mamao ma waena o nā hakahaka:
d sin θ = n λ
d (75.10-2) = (3)(5.10-7)
d (75.10-2) = 15.10-7
d = (15.10-7) / (75.10-2)
d = (15/75).10-5
d = (1/5)(10-5) nā mika
d = (0,2)(10-5) nā mika
d = 2.10-6 mika
ʻO C ka pane pololei.
11. He kukuna o ke kukui monochromatic me ka nalu o 500 nm (1 nano = 10 nm)-9) hele mai i luna i puka makaniInā hana ka mālamalama ʻehā i kahi kihi ʻokoʻa o 30o, ʻo ka helu o nā laina no kenimika o ka pūnaewele he….
- 3000
- 2500
- 1250
- 1000
- 250
Pahana
Ua ʻike ʻia:
Ka lōʻihi o ka nalu (λ) = 500.10-9 mika = 5.10-7 mika
θ = 30o
n = 4
Ua nīnau ʻia: ka helu o nā laina no kenimika o ka grid
Pane:
Ka mamao ma waena o nā hakahaka:
d sin θ = n λ
d (hewa 30o) = (4)(5.10-7)
d (0,5) = 20.10-7
d = (20.10-7) / 0,5
d = 40.10-7
d = 4.10-6 mika
Helu o nā laina no kenimika o ka pūnaewele:
x = 1 / 4.10-6 mika
x = 0,25.106 laina / mika
x = 0,25.106 laina / 102 cm
x = 0,25.104 laina / kenimika
x = 25.102 laina / kenimika
x = 2500 laina / kenimika
ʻO ka pane pololei ʻo B.
Puna Nīnau:
2015/2016 SMA/MA Physics UN nīnau
