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Referensi: Chapter 35, Halliday Resnick Ed. 9

Interferensi(Interference)

Intisari Materi

1. Prinsip Huygen (Huygens’Principle)

2. Panjang Gelombang dan Indeks Bias

3. Eksperimen Interferensi Young

4. Koherensi

5. Intensitas dari interferensi gelombang cahaya dari celah

ganda (2 celah)

6. Interferensi Lapisan Tipis (Thin-Film)

7. Interferometer Michelson

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Interferensi dalam kajian Fisika.

Dikaji: Interferensi optika Yaitu Interferensi gelombang (cahaya).

Contoh Interferensi:

Kupu-kupu Morpho memiliki warna biru di permukaan sayap karena interferensi optika,

ada spektrum (rentang warna cahaya) biru berbeda.

(Sumber :Philippe Colombi/PhotoDisc//Getty Images)

1 Prinsip Huygen

Dalam penjalaran gelombang cahaya,

tiap titik pada muka gelombang

(wavefront) dapat dianggap sebagai

sumber cahaya yang menyebar

secara sferis (penyebaran berbentuk

bola atau lengkungan). Setelah waktu

t di posisi baru tiap titik temu garis

singgung lengkungan cahaya tersebut

membentuk muka gelombang

(wavefront) baru dan seterusnya.

Christiaan Huygens, matematikawan dan fisikawan Belanda

Lahir di Den Haag, Belanda, 14 April 1629 – meninggal di

Belanda, 8 Juli 1695 pada umur 66 tahun)

Cahaya sebagai Gelombang

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Cahaya Sebagai Gelombang

Hukum Pembiasan (Law of Refraction):Pembiasan gelombang cahaya yang

berbentuk gelombang bidang (plane

wave) melalui batas dua medium berbeda

udara (air) dan kaca (glass)----seperti

dijelaskan Huygen bagaimana setiap titik

cahaya menyebar.

Panjang gelombang (wavelength) cahaya

di kaca lebih kecil dari pada di udara.

Sebetulnya ada juga peristiwa

pemantulan tapi untuk alas an kita focus

pada pembahasan efek pembiasan pada

gambar di samping tidak diilustrasikan.

Tiga tahap pembiasan (a) (b) (c)

Laju gelombang di udara lebih cepat

dari laju gelombang di dalam kaca

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Penurunan Hukum Pembiasan

Perhatikan segitiga

Waktu yang diperlukan oleh gelombang

menjalar di medium ke 1 (udara)

Waktu yang diperlukan oleh gelombang

menjalar di medium ke 2 (kaca)

Pada selang waktu yang sama gelombang menjalar melalui medium berbeda

Penurunan Hukum Pembiasan

Definisikan besaran indeks bias (n)

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Cahaya sebagai Gelombang

2 Panjang Gelombang dan Indeks Bias

• Ketika cahaya melalui medium berbeda, panjang gelombang cahaya berubah

sebab laju perambatan gelombang cahaya berubah.

• Laju gelombang cahaya bergantung indeks bias medium yang dilaluinya.

GELOMBANG MONOKROMATIK

panjang gelombang monokromatik yang menjalar

di ruang vakum dengan laju c

panjang yang menjalar di medium dengan indeks bias n

dengan laju v

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Beda fasa (phase difference) antara dua gelombang cahaya dapat berubah

Jika gelombang gelombang tersebut melalui material yang berbeda dengan indeks

bias berbeda.

Definisikan N sebagai

Example, Phase difference of two waves due to difference in refractive indices:

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35.3: Diffraction:

If a wave encounters a barrier that has an opening of

dimensions similar to the wavelength, the part of the

wave that passes through the opening will flare

(spread) out—will diffract—into the region beyond

the barrier. The flaring is consistent with the

spreading of wavelets according to Huygens

principle. Diffraction occurs for waves of all types.

35.3: Diffraction:

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35.4: Young’s Interference Experiment:

35.4: Young’s Interference Experiment:

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35.4: Young’s Interference Experiment, Location of Fringes:

35.4: Young’s Interference Experiment, Location of Fringes:

For a bright fringe, ∆L must be either

zero or an integer number of

wavelengths. Therefore,

For a dark fringe, ∆L must be an odd

multiple of half a wavelength.

Therefore,

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Example, Double-slit Interference Pattern:

Example, Double-slit interference pattern:

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35.5: Coherence:

For the interference pattern to appear

on viewing screen C in the figure, the

light waves reaching any point P on the

screen must have a phase difference

that does not vary in time. When the

phase difference remains constant, the

light from slits S1 and S2 is said to be

completely coherent.

If the light waves constantly change in

time, then the light is said to be

incoherent.

35.6: Intensity in Double-Slit Interference:

The electric field components of the light waves at point P on the screen can be written as:

The intensity of the pattern at P can be expressed as:

And the phase difference can be expressed as:

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35.6: Intensity in Double-Slit Interference:

For a maximum

For a minimum,

35.6: Intensity in Double-Slit Interference, Some Proofs:

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Example, Combining three light waves by using phasors:

35.7: Interference from Thin Films:

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35.7: Interference from Thin Films:

35.7: Interference from Thin Films, Reflection Phase Shifts:

For light, when an incident wave traveling in the medium of greater index of refraction n is

reflected at the interface separating the second medium of smaller refractive index, the

reflected wave does not undergo a change in phase; that is, its reflection phase shift is zero.

When a wave traveling in a medium of smaller index of refraction is reflected at the

interface separating the second medium of a higher refractive index, the phase change is π

rad, or half a wavelength.

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35.7: Interference from Thin Films, Equations:At point a on the front interface, the incident wave

(in air) reflects from the medium having the higher

of the two indexes of refraction; so the wave of

reflected ray r1 has its phase shifted by 0.5

wavelength.

At point b on the back interface, the incident wave

reflects from the medium (air) having the lower of

the two indexes of refraction; the wave reflected

there is not shifted in phase by the reflection, and

thus neither is the portion of it that exits the film as

ray r2.If the waves of r1 and r2 are to be exactly in phase so that they produce fully constructive

interference, the path length 2L must cause an additional phase difference of 0.5, 1.5, 2.5,

…wavelengths.

If, instead, the waves are to be exactly out of phase so that there is fully destructive interference,

the path length 2L must cause either no additional phase difference or a phase difference of 1, 2,

3, . . . wavelengths. But

35.7: Interference from Thin Films, Equations:

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35.7: Interference from Thin Films,

Film thickness much less than λ:

Example, Thin-film interference of a water film in air:

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Example, Thin-film interference of a coating on a glass lens:

Example, Thin-film interference:

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Example, Thin-film interference, cont.:

Example, Thin-film interference, cont.:

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35.8: Michelson’s Interferometer:

If the material has thickness L and index of

refraction n, then the number of wavelengths along

the light’s to-and-fro path through the material is

The number of wavelengths in the same thickness

2L of air before the insertion of the material is

When the material is inserted, the light returned

from mirror M1 undergoes a phase change (in terms

of wavelengths) of

For each phase change of one wavelength, the

fringe pattern is shifted by one fringe. Thus, by

counting the number of fringes through which the

material causes the pattern to shift, one can

determine the thickness L of the material in terms

of λ.