Chapter 22. Wave Optics Light is an electromagnetic wave. The interference of light waves produces the colors reflected from a CD, the iridescence of bird feathers, and the technology underlying supermarket checkout scanners and optical computers. Chapter Goal: To understand and apply the wave model of light. 1/27/09 1

Models of Light

• The wave model: under many circumstances, light exhibits the same behavior as sound or water waves. The study of light as a wave is called wave optics.

• The ray model: The properties of prisms, mirrors, and lenses are best understood in terms of light rays. The ray model is the basis of ray optics.

• The photon model: In the quantum world, light behaves like neither a wave nor a particle. Instead, light consists of photons that have both wave-like and particle-like properties. This is the quantum theory of light.

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Wave propagation

• Diffraction: A wave passing through an aperture spreads out. The effect is pronounced if the aperture size is comparable to a wavelength.

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Ray model works for wavelength<<aperture size

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Diffraction of light

Light diffraction is observed for slits smaller than a micron or so. The wavelength of light (about 0.5 micron = 0.5e-6 m depending on the color) can be inferred from the pattern.

A laser is a source of harmonic (monochromatic) light waves. 1/27/09 4

Aperture sources of waves

An aperture with width small compared to the wavelength behaves as a source of circular waves driven in phase by the incident wave.

Multiple apertures are coherent sources.

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Two slit interference of waves

Two coherent wave sources produce an interference pattern.

Two slits driven by the same incident wave result in an interference pattern.

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Huygen’s Principle Wave propagation can

be modeled by treating each element of an advancing wave front as a source of spherical waves and an aperture as a collection of elements. In this way, the diffraction pattern of any aperture shape may be computed.

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Diffraction through a slit

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Circular-Aperture Diffraction Light of wavelength λ passes through a circular aperture of diameter D, to a screen a distance L behind the aperture, L>>D. The diffraction pattern has a circular central maximum, surrounded by a series of secondary rings. The angle of the first minimum in the intensity is

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Example

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Double slit interference Double slit interference of light is a simple and important case.

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Geometry of double slit interference

Constructive interference if path length difference is a multiple of a wavelength:

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Example of double slit interference

QUESTION: A laser of wavelength l = 500 nm illuminates a pair of slits separated by d= 1.0 mm. What is the angle of the m=1 maximum in radians?

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EXAMPLE:

QUESTION: A laser of wavelength l = 500 nm illuminates a pair of slits separated by d= 1.0 mm. What is the angle of the m=1 maximum in radians?

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A. They fade out and disappear. B. They get out of focus. C. They get brighter and closer together. D. They get brighter and farther apart. E. They get brighter but otherwise do not change.

Suppose the viewing screen in the figure is moved closer to the double slit. What happens to the interference fringes?

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A. They fade out and disappear. B. They get out of focus. C.  They get brighter and closer together. D. They get brighter and farther apart. E. They get brighter but otherwise do not change.

Suppose the viewing screen in the figure is moved closer to the double slit. What happens to the interference fringes?

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The Diffraction Grating A multi-slit (or multi reflection or refraction) device is called a diffraction grating. Bright fringes will occur at angles θm, such that

The y-positions of these fringes will occur at

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Fully constructive interference at the same angles as for two slits. But the amplitude at a maximum is N times that of a single slit and the angular width of the peaks is much smaller => much more precise focusing of the wave energy.

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Figure 22.8 (a) shows the narrow bright fringes produced by a grating.

Figure 22.8 (b) shows how a mix of light of different wavelength can be separated into its components and analyzed with the aid of a grating.

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Example of use of diffraction grating

QUESTION:

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EXAMPLE 22.3 Measuring wavelengths emitted by sodium atoms

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Michelson interferometer A Michelson interferometer splits light into two beams which reflect off mirrors and recombine exhibiting interference. Moving mirror M2 and changing the path length of one beam, or delaying the light with some material will change the interference pattern. To an observer looking into the output beam, there are two coherent sources behind mirror 1. 1/27/09 22

Light of wavelength l1 illuminates a double slit, and interference fringes are observed on a screen behind the slits. When the wavelength is changed to l2, the fringes get closer together. How large is l2 relative to l1?

A.  l2 is smaller than l1. B.  l2 is larger than l1. C.  Cannot be determined from this information.

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Light of wavelength l1 illuminates a double slit, and interference fringes are observed on a screen behind the slits. When the wavelength is changed to l2, the fringes get closer together. How large is l2 relative to l1?

A.   l2 is smaller than l1. B.  l2 is larger than l1. C.  Cannot be determined from this information.

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White light passes through a diffraction grating and forms rainbow patterns on a screen behind the grating. For each rainbow, A. the red side is farthest from the center of the

screen, the violet side is closest to the center. B. the red side is closest to the center of the screen,

the violet side is farthest from the center. C. the red side is on the left, the violet side on

the right. D. the red side is on the right, the violet side on

the left. 1/27/09 25

White light passes through a diffraction grating and forms rainbow patterns on a screen behind the grating. For each rainbow, A.   the red side is farthest from the center of the

screen, the violet side is closest to the center. B.  the red side is closest to the center of the screen,

the violet side is farthest from the center. C.  the red side is on the left, the violet side on

the right. D.  the red side is on the right, the violet side on

the left. 1/27/09 26

A Michelson interferometer using light of wavelength l has been adjusted to produce a bright spot at the center of the interference pattern. Mirror M1 is then moved distance l toward the beam splitter while M2 is moved distance l away from the beam splitter. How many bright-dark-bright fringe shifts are seen?

A.  4 B.  3 C.  2 D.  1 E.  0

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A.   4 B.  3 C.  2 D.  1 E.  0

A Michelson interferometer using light of wavelength l has been adjusted to produce a bright spot at the center of the interference pattern. Mirror M1 is then moved distance l toward the beam splitter while M2 is moved distance l away from the beam splitter. How many bright-dark-bright fringe shifts are seen?

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