Kamis, 19 Februari 2009

Gelombang dan Optik

Optics

From Wikipedia, the free encyclopedic

By:
Arip Nurahman
Department of Physics
Faculty of Sciences and Mathematics, Indonesia University of Education

and

Follower Open Course Ware at Massachusetts Institute of Technology
Cambridge, USA
Department of Physics
http://web.mit.edu/physics/
http://ocw.mit.edu/OcwWeb/Physics/index.htm
&
Aeronautics and Astronautics Engineering
http://web.mit.edu/aeroastro/www/
http://ocw.mit.edu/OcwWeb/Aeronautics-and-Astronautics/index.htm

For the book by Sir Isaac Newton, see Opticks.

Table of Opticks, 1728 Cyclopaedia

Optics (from ὀπτική, appearance or look in Ancient Greek) is the science that describes the behavior and properties of light and the interaction of light with matter. Optics explains optical phenomena.

The field of optics usually describes the behavior of visible, infrared, and ultraviolet light; however because light is an electromagnetic wave, similar phenomena occur in X-rays, microwaves, radio waves, and other forms of electromagnetic radiation and analogous phenomena occur with charged particle beams. Optics can largely be regarded as a sub-field of electromagnetism. Some optical phenomena depend on the quantum nature of light relating some areas of optics to quantum mechanics. In practice, the vast majority of optical phenomena can be accounted for using the electromagnetic description of light, as described by Maxwell's Equations.

The field of optics has its own identity, societies, and conferences. The pure science aspects of the field are often called optical science or optical physics. Applied optical sciences are often called optical engineering. Applications of optical engineering related specifically to illumination systems are called illumination engineering. Each of these disciplines tends to be quite different in its applications, technical skills, focus, and professional affiliations. More recent innovations in optical engineering are often categorized as photonics or optoelectronics. The boundaries between these fields and "optics" are often unclear, and the terms are used differently in different parts of the world and in different areas of industry.

Because of the wide application of the science of "light" to real-world applications, the areas of optical science and optical engineering tend to be very cross-disciplinary. Optical science is a part of many related disciplines including electrical engineering, physics, psychology, medicine (particularly ophthalmology and optometry), and others. Additionally, the most complete description of optical behavior, as known to physics, is unnecessarily complicated for most problems, so particular simplified models are used. These limited models adequately describe subsets of optical phenomena while ignoring behavior irrelevant and/or undetectable to the system of interest.

1 Classical optics

1.1 Topics related to classical optics

2 Modern optics

2.1 Topics related to modern optics

Classical optics

Before quantum optics became important, optics consisted mainly of the application of classical electromagnetism and its high frequency approximations to light. Classical optics divides into two main branches: geometric optics and physical optics.

Geometric optics, or ray optics, describes light propagation in terms of "rays". Rays are bent at the interface between two dissimilar media, and may be curved in a medium in which the refractive index is a function of position. The "ray" in geometric optics is an abstract object, or "instrument," which is perpendicular to the wavefronts of the actual optical waves. Geometric optics provides rules for propagating these rays through an optical system, which indicates how the actual wavefront will propagate. This is a significant simplification of optics, and fails to account for many important optical effects such as diffraction and polarization. It is a good approximation, however, when the wavelength is very small compared with the size of structures with which the light interacts. Geometric optics can be used to describe the geometrical aspects of imaging, including optical aberrations.

Geometric optics is often simplified even further by making the paraxial approximation, or "small angle approximation." The mathematical behavior then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics and paraxial raytracing, which are used to find first-order properties of optical systems, such as approximate image and object positions and magnifications. Gaussian beam propagation is an expansion of paraxial optics that provides a more accurate model of coherent radiation like laser beams. While still using the paraxial approximation, this technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics.

Physical optics or wave optics builds on Huygens's principle and models the propagation of complex wavefronts through optical systems, including both the amplitude and the phase of the wave. This technique, which is usually applied numerically on a computer, can account for diffraction, interference, and polarization effects, as well as other complex effects. Approximations are still generally used, however, so this is not a full electromagnetic wave theory model of the propagation of light. Such a full model is much more computationally demanding, but can be used to solve small-scale problems that require this more accurate treatment.

Topics related to classical optics

Modern optics

Modern optics encompasses the areas of optical science and engineering that became popular in the 20th century. These areas of optical science typically relate to the electromagnetic or quantum properties of light but do include other topics.

Topics related to modern optics

Other optical fields

Everyday optics

Optics is part of everyday life. Rainbows and mirages are examples of optical phenomena. Many people benefit from eyeglasses or contact lenses, and optics are used in many consumer goods including cameras. Superimposition of periodic structures, for example transparent tissues with a grid structure, produces shapes known as moiré patterns. Superimposition of periodic transparent patterns comprising parallel opaque lines or curves produces line moiré patterns.

References

Born, Max;Wolf, Emil. Principles of Optics (7th ed.). Pergamon Press, 1999.
Hecht, Eugene (2001). Optics (4th ed.). Pearson Education. ISBN 0-8053-8566-5.
Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks/Cole. ISBN 0-534-40842-7.
Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
Lipson, Stephen G. (1995). Optical Physics (3rd ed.). Cambridge University Press. ISBN 0-5214-3631-1.

External links

Optics

Textbooks and tutorials

Optics — an open-source Optics textbook
Optics2001 — Optics library and community

Societies

Terima Kasih, Semoga Bermanfaaat!

Selasa, 17 Februari 2009

Gelombang dan Optik

Gelombang dan Optik

Merupakan Kumpulan Materi Kuliah Gelombang dan Optik

Gelombang Optik

4 SKS

Dosen:

1. Dr. Andhy Setiawan, S.Pd., M.Si.

2. Lina Aviyanti, S.Pd., M.Si.

Sumber Buku:

Drs. Taufik Ramlan Ramalis, M.Si.

1. Osilasi Harmonis

a. Pendahuluan

Dunia kita ini penuh dengan benda-benda yang bergerak. Gerak-gerak tersebut dapat kita kelompokkan menjadi dua, yaitu gerak disekitar suatu tempat, dan gerak yang berpindah dari suatu tempat ke tempat lain.

Osilasi adalah variasi periodik - umumnya terhadap waktu - dari suatu hasil pengukuran, contohnya pada ayunan bandul. Istilah vibrasi sering digunakan sebagai sinonim osilasi, walaupun sebenarnya vibrasi merujuk pada jenis spesifik osilasi, yaitu osilasi mekanis. Osilasi tidak hanya terjadi pada suatu sistem fisik, tapi bisa juga pada sistem biologi dan bahkan dalam masyarakat. Osilasi terbagi menjadi 2 yaitu osilasi harmonis sederhana dan osilasi harmonis kompleks. Dalam osilasi harmonis sederhana terdapat gerak harmonis sederhana.

Gerak Harmonik Sederhana

Gerak Harmonik Sederhana (GHS) adalah gerak periodik dengan lintasan yang ditempuh selalu sama (tetap). Gerak Harmonik Sederhana mempunyai persamaan gerak dalam bentuk sinusoidal dan digunakan untuk menganalisis suatu gerak periodik tertentu. Gerak periodik adalah gerak berulang atau berosilasi melalui titik setimbang dalam interval waktu tetap. Gerak Harmonik Sederhana dapat dibedakan menjadi 2 bagian, yaitu :

Gerak Harmonik Sederhana (GHS) Linier, misalnya penghisap dalam silinder gas, gerak osilasi air raksa / air dalam pipa U, gerak horizontal / vertikal dari pegas, dan sebagainya.
Gerak Harmonik Sederhana (GHS) Angular, misalnya gerak bandul/ bandul fisis, osilasi ayunan torsi, dan sebagainya.

Beberapa Contoh Gerak Harmonik

Gerak harmonik pada bandul: Sebuah bandul adalah massa (m) yang digantungkan pada salah satu ujung tali dengan panjang l dan membuat simpangan dengan sudut kecil. Gaya yang menyebabkan bandul ke posisi kesetimbangan dinamakan gaya pemulih yaitu dan panjang busur adalah Kesetimbangan gayanya. Bila amplitudo getaran tidak kecil namun tidak harmonik sederhana sehingga periode mengalami ketergantungan pada amplitudo dan dinyatakan dalam amplitudo sudut
Gerak harmonik pada pegas: Sistem pegas adalah sebuah pegas dengan konstanta pegas (k) dan diberi massa pada ujungnya dan diberi simpangan sehingga membentuk gerak harmonik. Gaya yang berpengaruh pada sistem pegas adalah gaya Hooke,

b. Sistem Osilasi dengan Satu Derajat Kebebasan

1. Sifat Osilasi

2. Osilasi Harmonik Sederhana

3. Osilasi Teredam

4. Osilasi Teredam dengan Gaya Pemacu

c. Sistem Osilasi dengan Dua Derajat Kebebasan: Osilasi Gandeng

1. Osilasi Gandeng Pegas

2. Osilasi Gandeng Rangkaian LC

3. Sistematika Solusi Sistem Dua Derajat Kebebasan

d. Analisis Osilasi Harmonis

e. Soal Latihan

Universal oscillator equation

The equation

$\frac{\mathrm{d}^2q}{\mathrm{d} \tau^2} + 2 \zeta \frac{\mathrm{d}q}{\mathrm{d}\tau} + q = 0$

is known as the universal oscillator equation since all second order linear oscillatory systems can be reduced to this form. This is done through nondimensionalization.

If the forcing function is f(t) = cos(ωt) = cos(ωt_cτ) = cos(ωτ), where ω = ωt_c, the equation becomes

$\frac{\mathrm{d}^2q}{\mathrm{d} \tau^2} + 2 \zeta \frac{\mathrm{d}q}{\mathrm{d}\tau} + q = \cos(\omega \tau).$

The solution to this differential equation contains two parts, the "transient" and the "steady state".

Transient solution

The solution based on solving the ordinary differential equation is for arbitrary constants c₁ and c₂

$\text{[math]}$ 1 \ \mbox{(overdamping)} \\ e^{-\zeta\tau} (c_1+c_2 \tau) = e^{-\tau}(c_1+c_2 \tau) & \zeta = 1 \ \mbox{(critical damping)} \\ e^{-\zeta \tau} \left[ c_1 \cos \left(\sqrt{1-\zeta^2} \tau\right) +c_2 \sin\left(\sqrt{1-\zeta^2} \tau\right) \right] & \zeta < src="http://upload.wikimedia.org/math/f/6/5/f65c05c1aed77ef6082d00a66f0d63dc.png" style="border-top-style: none; border-right-style: none; border-bottom-style: none; border-left-style: none; border-width: initial; border-color: initial; vertical-align: middle; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">

The transient solution is independent of the forcing function. If the system is critically damped, the response is independent of the damping.

Equivalent systems

Harmonic oscillators occurring in a number of areas of engineering are equivalent in the sense that their mathematical models are identical (see universal oscillator equation above). Below is a table showing analogous quantities in four harmonic oscillator systems in mechanics and electronics. If analogous parameters on the same line in the table are given numerically equal values, the behavior of the oscillators will be the same.

Translational Mechanical	Torsional Mechanical	Series RLC Circuit	Parallel RLC Circuit
Position $x\,$	Angle $\theta\,\!$	Charge $q\,$	Voltage $e\,$
Velocity $\frac{dx}{dt}\,$	Angular velocity $\frac{d\theta}{dt}\,$	Current $\frac{dq}{dt}\,$	$\frac{de}{dt}\,$
Mass $M\,$	Moment of inertia $I\,$	Inductance $L\,$	Capacitance $C\,$
Spring constant $K\,$	Torsion constant $\mu\,$	Elastance $1/C\,$	Susceptance $1/L\,$
Friction $\gamma\,$	Rotational friction $\Gamma\,$	Resistance $R\,$	Conductance $1/R\,$
Drive force $F(t)\,$	Drive torque $\tau(t)\,$	$e\,$	$di/dt\,$
Undamped resonant frequency $f_n\,$ :
$\frac{1}{2\pi}\sqrt{\frac{K}{M}}\,$	$\frac{1}{2\pi}\sqrt{\frac{\mu}{I}}\,$	$\frac{1}{2\pi}\sqrt{\frac{1}{LC}}\,$	$\frac{1}{2\pi}\sqrt{\frac{1}{LC}}\,$
Differential equation:
$M\ddot x + \gamma\dot x + Kx = F\,$	$I\ddot \theta + \Gamma\dot \theta + \mu \theta = \tau\,$	$L\ddot q + R\dot q + q/C = e\,$	$C\ddot e + \dot e/R + e/L = \dot i\,$