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Wave Optics

In optics, wave optics is a study of physical optics which focuses on the study of waves in optical systems and how they are affected by the device's geometrical structure and optical properties. Wave optics is a topic that is often taught in higher-level courses in optics. Wave optics is very important in the study of optical devices, including microscopes, telescopes, laser devices, and cameras. A simple wave optical system is a waveguide with a single input and a single output. Most waveguides are designed to contain a certain number of modes, which are linearly independent solutions of Maxwell's equations for the waveguide. These modes are usually degenerate, meaning that they have the same frequency, but different group velocities and different behavior in the time domain. For example, a waveguide with a single input and one output is a single-mode waveguide. The modes are all linearly independent solutions of the wave equation. A waveguide with two inputs and a single output is also typically a single-mode waveguide. A waveguide with two inputs and two outputs is usually a higher-order mode, meaning that it is not a linearly independent solution of the wave equation. Higher order modes can be split into their linearly independent components. The situation is analogous to the sum of a set of identical waves. The complete wave equation can be split into the equations for the individual waves, and a solution of the wave equation can be found for each of these separate waves. Each of these wave solutions is an individual mode, which in turn can be split into linearly independent solutions. When the number of modes in the waveguide is greater than one, the waveguide is referred to as a resonant waveguide. The vibrational behavior of a resonant waveguide can be described using the concept of a resonant frequency. The resonant frequency, or simply the resonant frequency, of a resonant waveguide is the frequency at which a single mode of the waveguide is tuned, or resonant. For example, a resonant waveguide with a ring-shaped cross-section is a waveguide with two modes, and the resonant frequency is the frequency at which the waveguide is tuned between the two modes.

Interference

135 Practice Problems
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03:49
Principles of Physics a Calculus Based Text

In the double-slit arrangement of Figure P27.10 , $d=0.150 \mathrm{mm}, L=140 \mathrm{cm}, \lambda=643 \mathrm{nm},$ and $y=1.80 \mathrm{cm}$ (a) What is the path difference $\delta$ for the rays from the two slits arriving at $P$ ? (b) Express this path difference in terms of $\lambda$. (c) Does $P$ correspond to a maximum, a minimum, or an intermediate condition? Give evidence for your answer.

Wave Optics
02:18
Principles of Physics a Calculus Based Text

Two slits are separated by $0.320 \mathrm{mm} .$ A beam of 500 -nm light strikes the slits, producing an interference pattern. Determine the number of maxima observed in the angular range $-30.0^{\circ} \leq \theta \leq 30.0^{\circ}$.

Wave Optics
01:53
Principles of Physics a Calculus Based Text

A Young's interference experiment is performed with blue-green argon laser light. The separation between the slits is $0.500 \mathrm{mm},$ and the screen is located $3.30 \mathrm{m}$ from the slits. The first bright fringe is located $3.40 \mathrm{mm}$ from the center of the interference pattern. What is the wavelength of the argon laser light?

Wave Optics

Young’s Double-Slit Experiment

88 Practice Problems
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02:17
Principles of Physics a Calculus Based Text

slits are illuminated with coherent 600 -nm light. Calculate the distance $y$ from the central maximum for which the average intensity on the screen is $75.0 \%$ of the maximum.

Wave Optics
04:07
Principles of Physics a Calculus Based Text

In a location where the speed of sound is $343 \mathrm{m} / \mathrm{s}$, a $2000-\mathrm{Hz}$ sound wave impinges on two slits $30.0 \mathrm{cm}$ apart. (a) At what angle is the first maximum of sound intensity located? (b) What If ? If the sound wave is replaced by 3.00 -cm microwaves, what slit separation gives the same angle for the first maximum of microwave intensity? (c) What If? If the slit separation is $1.00 \mu \mathrm{m},$ what frequency of light gives the same angle to the first maximum of light intensity?

Wave Optics
04:34
Principles of Physics a Calculus Based Text

Young's double-slit experiment underlies the instrument landing system used to guide aircraft to safe landings at some airports when the visibility is poor. Although real systems are more complicated than the example described here, they operate on the same principles. A pilot is trying to align her plane with a runway as suggested in Figure P27.2. Two radio antennas (the black dots in the figure are positioned adjacent to the runway, separated by $d=40.0 \mathrm{m} .$ The antennas broadcast unmodulated coherent radio waves at $30.0 \mathrm{MHz}$. The red lines in Figure P27.2 represent paths along which maxima in the interference pattern of the radio waves exist. (a) Find the wavelength of the waves. The pilot "locks onto" the strong signal radiated along an interference maximum and steers the plane to keep the received signal strong. If she has found the central maximum, the plane will have precisely the correct heading to land when it reaches the runway as exhibited by plane $\mathrm{A}$. (b) What If? Suppose the plane is flying along the first side maximum instead as is the case for plane $\mathrm{B}$. How far to the side of the runway centerline will the plane be when it is $2.00 \mathrm{km}$ from the antennas, measured along its direction of travel? (c) It is possible to tell the pilot that she is on the wrong maximum by sending out two signals from each antenna and equipping the aircraft with a two-channel receiver. The ratio of the two frequencies must not be the ratio of small integers (such as $\frac{3}{4}$ ). Explain how this two-frequency system would work and why it would not necessarily work if the frequencies were related by an integer ratio.

Wave Optics

Diffraction Patterns

131 Practice Problems
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01:43
Inorganic Chemistry

The structures of $\mathrm{TeF}_{4}$ and $\mathrm{TeCl}_{4}$ in the gas phase have been studied by electron diffraction (S. A. Shlykov, N. I. Giricheva, A. V. Titov, M. Szwak, D. Lentz, G. V. Girichev, Dalton Trans., 2010,39,3245 ).
a. Would you expect the Te-X (axial) distances in these molecules to be longer or shorter than than $\mathrm{Te}-\mathrm{X}$ (cquatorial) distances? Explain briefly.
b. Which compound would you predict to have the smaller $X(\text { axial })-$ Te $-X(\text { axial })$ angles? The smaller X(equatorial) - Te-X(equatorial) angles? Explain briefly.

Simple Bonding Theory
01:52
Physical Chemistry

What is the equation for the distances between 110 planes for a crystal with mutually perpendicular axes?

Solid-State Chemistry
Madi Sousa
01:07
21st Century Astronomy

When viewed by radio telescopes, Jupiter is the second-brightest object in the sky. What is the source of its radiation?

Worlds of Gas and Liquid-The Giant Planets

Resolution of Single-Slit and Circular Apertures

45 Practice Problems
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02:30
21st Century Astronomy

You are shopping for telescopes online. You find two in your price range. One of these has an aperture of $20 \mathrm{cm},$ and the other has an aperture of $30 \mathrm{cm} .$ If aperture size is the only difference, which should you choose, and why?
a. The $20 \mathrm{cm}$, because the light-gathering power will be better.
b. The $20 \mathrm{cm}$, because the image size will be larger.
c. The $30 \mathrm{cm}$, because the light-gathering power will be better.
d. The $30 \mathrm{cm}$, because the image size will be larger.

The Tools of the Astronomer
Matthew Miranda
00:48
University Physics

Does Huygens's principle apply to all types of waves?

The Nature of Light
Mayukh Banik
02:49
University Physics

A single slit of width 0.1 mm is illuminated by a mercury light of wavelength 576 nm. Find the intensity at a $10^{\circ}$ angle to the axis in terms of the intensity of the central maximum.

Diffraction
Donald Albin

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