Difraksi Cahaya Dede Djuhana Kuliah Fisika Dasar 2 Fakultas Teknik – Kelas FD2_06 Universitas Indonesia 2011 Department of Physics University of Indonesia
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Pendahuluan • Difraksi adalah peristiwa pembelokan arah ram bat gelombang yang melalui suatu celah sempit. • Timbul pola terang dan gelap dimana intensitas pola terang tidak sama atau makin jauh makin ke cil intensitasnya
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Macam-macam Difraksi Difraksi Franhofer
Difraksi Fresnel
Cahaya jauh dari celah sehingga cahaya yang masuk sejajar Celah sempit lebar celah << jarak celah-layar
Jarak sumber cahaya ke celah dekat Berkas cahaya tidak perlu sejajar Lebar celah besar
Celah tunggal Lubang bulat (circular aperture) Dua celah Kisi (celah banyak)
berbentuk lingkaran Lubang berbentuk persegi Penghalang berbentuk piringan Penghalang berbentuk tajam (lancip
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Difraksi Fraunhofer Celah Tunggal
sin θ gelap = m
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λ a
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Intensitas Celah Tunggal Fraunhofer Celah tunggal diasumsikan terdir i dari daerah kecil dengan lebar Δy
∆β
∆β =
2π
Perubahan medan (Listrik) yang berhubungan ∆y
2π
2π
∆y sin θ β = N ∆β = λ N ∆y sin θ = λ a sin θ λ
a = N ∆y
2π =
2π
λ
a sin θ gelap
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β
ER / 2 sin = 2 R β
E0 ER = 2R sin = 2 2 2
sin β = E sin ( β / 2) 2 0 β / 2
sin( β / 2) (π a sin θ / λ ) = = I max sin β / 2 π a sin θ / λ 2
I = I max
ER=Amplitudo gelomb ang (medan listrik)
I max
(θ = 0° )
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Terang pusat
π a sin θ = mπ → minimum λ sin θ gelap = m
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λ
a 6
Kurva Intensitas Difraksi
sin( β / 2) (π a sin θ / λ ) = = I sin max π a sin θ / λ β / 2 2
I = I max
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Difraksi celah ganda (double slit) π d sin θ I = I max cos λ
sin (π a sin θ / λ ) π a sin θ / λ
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d sin θ mλ d = → =m a sin θ λ a d=jarak antar celah a=lebar celah
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Resolusi celah tunggal
Kriteria Rayleigh
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Resolusi slit berbentuk lingkaran (circular) λ θ = 1,22 a
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Resolusi mata (eye resolution) • Let us choose a wavelength of 500 nm, near the center of the visible spe ctrum. Although pupil diameter varies from person to person, we esti mate a daytime diameter of 2 mm. We use
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Kisi Difraksi
• Side view of a diffraction grating. The slit separation is d, and the path difference be tween adjacent slits is d sin θ.
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• Diagram of a diffraction grating spectrometer. The collimated beam inci dent on the grating is spread into its various wavelength components w ith constructive interference for a particular wavelength occurring at th e angles ! bright that satisfy the equation d sin θ bright = mλ, where m = 0, 1, 2, . . . . Department of Physics University of Indonesia
Daya pisah pada kisi (Resolving power of t he diffraction grating) • The diffraction grating is useful for measuring wavelengths accuratel y. Like the prism, the diffraction grating can be used to separate white light into its wavelength components. Of the two devices, a grating wi th very small slit separation is more precise if one wants to distinguis h two closely spaced wavelengths. • For two nearly equal wavelengths λ1 and λ2 between which a diffracti on grating can just barely distinguish, the resolving power R of the gr ating is defined as
λ
λ = R= λ2 − λ1 ∆λ
λ=
λ1 + λ2 2
, ∆λ = λ1 − λ2
• Thus, a grating that has a high resolving power can distinguish small differences in wavelength. If N slits of the grating are illuminated, it c an be shown that the resolving power in the mth-order diffraction is R = Nm Department of Physics University of Indonesia
Difraksi pada kristal dengan X-ray
Tungsten (bcc)
d sin θ = mλ
Hukum Bragg
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a
b
• (a) A Laue pattern of a single crystal of the mineral beryl (berylliu m aluminum silicate). Each dot represents a point of constructive i nterference. (b) A Laue pattern of the enzyme Rubisco, produced with a wide-band x-ray spectrum. This enzyme is present in plant s and takes part in the process of photosynthesis. The Laue patter n is used to determine the crystal structure of Rubisco. Department of Physics University of Indonesia
