ch28 interference diffraction izzah

$: CH28 Interference Diffraction Izzah$
Copyright © 2010 Pearson Education, Inc.

NURUL IZZAH 2013Interference n diffractions

Chapter 28Physical Optics: Interference

and Diffraction

Animation courtesy of Dr. Dan Russell, Grad. Prog. Acoustics, Penn State



Course Outline

Towards the end of the lecture, students are expected to understand:– terminologies and definition of

superposition, interference, diffraction and resolutions.

– concepts of Young’s Two-slit experiment and diffractions.

– briefly about resolutions and diffraction gratings.



Units of Chapter 28

• Superposition and Interference• Young’s Two-Slit Experiment• Interference in Reflected Waves• Diffraction• Resolution **• Diffraction gratings **

** items will only be discussed briefly



28-1 Superposition and InterferenceIf two waves occupy the same space, their amplitudes add at each point. They may interfere either constructively or destructively.



28-1 Superposition and Interference

Interference is only noticeable if the light sources are monochromatic (so all the light has the same wavelength) and coherent (different sources maintain the same phase relationship over space and time).

If this is true, interference will be constructive where the two waves are in phase, and destructive where they are out of phase.



28-1 Superposition and InterferenceIn this illustration, interference will be constructive where the path lengths differ by an integral number of wavelengths, and destructive where they differ by a half-odd integral number of wavelengths.




To summarize, the two path lengths and will interfere constructively or destructively according to the following:

1 2



28-2 Young’s Two-Slit Experiment

In this experiment, the original light source need not be coherent; it becomes so after passing through the very narrow slits.




If light consists of particles, the final screen should show two thin stripes, one corresponding to each slit.

However, if light is a wave, each slit serves as a new source of “wavelets,” as shown, and the final screen will show the effects of interference. This is called Huygens’s principle.



28-2 Young’s Two-Slit ExperimentAs the pattern on the screen shows, the light on the screen has alternating light and dark fringes, corresponding to constructive and destructive interference.The path difference is given by:




The dark fringes are between the bright fringes; the condition for dark fringes is:

Therefore, the condition for bright fringes (constructive interference) is:

Above central bright fringe

Below central bright fringe




This diagram illustrates the numbering of the fringes.



EXAMPLE A.K.A EXERCISEExample 1 Young’s Double-Slit Experiment

Red light (664 nm) is used in Young’s experiment with slits separatedby 0.000120 m. The screen is located a distance 2.75 m from the slits.Find the distance on the screen between the central bright fringe andthe third-order bright fringe.



951.0m101.20m106643sinsin 4

911

dm

m 0456.0951.0tanm 75.2tan Ly


NURUL IZZAH 2013Interference n diffractions 28-3 Interference in Reflected WavesWaves that reflect from objects at different locations can interfere with one another.

Propagation

ReflectWall (object)

Interfere

Reflected waves change their phase in two ways:i. Proportion to distances of wave travel (light in two

slit experiment)ii. As a result of reflection process itself.


NURUL IZZAH 2013Interference n diffractions 28-3 Interference in Reflected Waves

Phase changes due to:

Reflection

Air wedge

Newton’s ringThin film

Interference in CDs


NURUL IZZAH 2013Interference n diffractions 28-3 Interference in Reflected WavesReflection:

There is no phase change when light reflects from a region with a lower index of refraction.

There is a half-wavelength phase change when light reflects from a region with a higher index of refraction, or from a solid surface.



Constructive interference:

Destructive interference:

Air wedge:

TouchSmall separation

air gap



28-3 Interference in Reflected Waves



28-3 Interference in Reflected WavesNewton’s ring:Replace top glass (air wedge) with curved glass (spherical cross section).

Result is a series of circular interference fringes called as Newton’s ring.

Closely spaced as d from

central



Thin film: Interference by thin films can be found in soap bubbles and oil slicks (shown in swirling pattern of color resulting from constructive/ destructive interference when white light reflects from a thin film).

Now, we have not only path differences and phase changes on reflection; we also must account for the change in wavelength as the light travels through the film.



Wavelength of light in a medium of index of refraction n:

Therefore, the condition for destructive interference, where t is the thickness of the film, is:



The condition for constructive interference:

The rainbow of colors we see is due to the different wavelengths of light.



The phase changes upon reflection depend on the indices of refraction of the film and the surrounding media:


NURUL IZZAH 2013Interference n diffractions 28-3 Interference in Reflected WavesCDs (compact disks):The signal is encoded as tiny bumps in the surface, andthe reflected laser beam varies in intensity depending on whether it is reflecting from a bump or not.


NURUL IZZAH 2013Interference n diffractions 28-4 Diffraction

A wave passing through a small opening will diffract (spread out), as shown. This means that, after the opening, there are waves traveling in directions other than the direction of the original wave.



To investigate the diffraction of light, we consider what happens when light passes through a very narrow slit. As the figure indicates, what we see on the screen is a single-slit diffraction pattern.


NURUL IZZAH 2013Interference n diffractions 28-4 DiffractionThis pattern is due to the difference in path length from different parts of the opening.

The first dark fringe occurs when:



The second dark fringe occurs when:

Generally:W sin θ =mλ



In general, then, we have for the dark fringes in a single-slit interference pattern:

The positive and negative values of m account for the symmetry of the pattern around the center.



28-4 Diffraction



• Light passes through a slit and shines on a flat screen that is located L=0.4nm away. the wavelength of the light in a vacuum is λ=410nm. The distance between midpoint of the central bright fringe and the first dark fringe is y. determine the width of central bright fringe when the width of slit is a. 5x10⁻⁶ m [0.66m]b. 2.5x10⁻⁶ m [0.13m]

Try this out…


NURUL IZZAH 2013Interference n diffractions 28-5 Resolution

Diffraction through a small circular aperture results in a circular pattern of fringes. This limits our ability to distinguish one object from another when they are very close.The location of the first dark fringe determines the size of the central spot:



Rayleigh’s criterion relates the size of the central spot to the limit at which two objects can be distinguished:If the first dark fringe of one circular diffraction pattern passes through the center of a second diffraction pattern, the two sources responsible for the patterns will appear to be a single source.

The size of the spot increases with wavelength, and decreases with the size of the aperture.



On the left, there appears to be a single source; on the right, two sources can be clearly resolved.


NURUL IZZAH 2013Interference n diffractions 28-6 Diffraction Gratings

A system with a large number of slits is called a diffraction grating.As the number of slits grows, the peaks become narrower and more intense. Here is the diffraction pattern for five slits:



The positions of the peaks are different for different wavelengths of light.The condition for constructive interference in a diffraction grating:



There are many ways to construct diffraction gratings.

This acoustic-optic modulator diffracts light from acoustic wavefronts in the crystal. Turning the sound off eliminates the signal; changing the sound frequency modifies it.


NURUL IZZAH 2013Interference n diffractions 28-6 Diffraction GratingsX-ray diffraction is used to determine crystal structure – the spacing between crystal planes is close enough to the wavelength of the X-rays to allow diffraction patterns to be seen.

A grating spectroscope allows precise determination of wavelength:



Diffraction can also be observed upon reflection from narrowly-spaced reflective grooves; the most familiar example is the recorded side of a CD. Some insect wings also display reflective diffraction, especially butterfly wings.


NURUL IZZAH 2013Interference n diffractions Summary of Chapter 28• When two waves are superposed, the result

may be either constructive or destructive interference.

• Monochromatic light consists of a single frequency.

• Coherent light maintains a constant phase relationship.

• Young’s two-slit experiment shows light and dark interference fringes.


NURUL IZZAH 2013Interference n diffractions Summary of Chapter 28

• Bright fringes:

• Dark fringes:

• Thin films can form colors in reflected light through the destructive interference of other colors.



• When a wave encounters an obstacle or opening, it changes direction. This is called diffraction.

• When monochromatic light passes through a narrow slit, a pattern of bright and dark fringes is produced.

• Dark fringes (W is the width of the slit):



• Resolution is the ability to distinguish closely spaced objects. Diffraction limits resolution.

• Rayleigh’s criterion: if two objects are separated by less than the minimum angle, they cannot be distinguished:

• A diffraction grating is a large number of small slits. Principal maxima:

ch28 interference diffraction izzah

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