chapter 28 physical optics: interference and...
TRANSCRIPT
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Overview of Chapter 28
• Superposition and Interference
• Young’s Two-Slit Experiment
• Interference in Reflected Waves
• Diffraction
• Resolution
• Diffraction Gratings
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28-1 Superposition and Interference
If two waves occupy the same space, their amplitudes add at each point. They may interfere either constructively or destructively.
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28-1 Superposition and Interference
• Interference is only noticeable if:
- 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).
• Interference will be constructive where the two waves are in phase, and destructive where they are out of phase.
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28-1 Superposition and Interference
In this illustration:
• Interference will be constructive where the path lengths differ by an integral number of wavelengths.
• Destructive where they differ by a half-odd integral number of wavelengths.
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28-1 Superposition and Interference
Two path lengths will thus interfere constructively or destructively according to the following:
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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.
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28-2 Young’s Two-Slit Experiment
• If light consists of particles..
- The final screen should show two thin stripes, one corresponding to each slit.
• If light is a wave…
- Each slit serves as a new source of “wavelets”
- Final screen will show the effects of interference.
- This is called Huygens’s principle.
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28-2 Young’s Two-Slit Experiment
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:
Therefore, the condition for bright fringes (constructive interference) is:
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28-2 Young’s Two-Slit Experiment
The dark fringes are between the bright fringes; the condition for dark fringes is:
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28-3 Interference in Reflected WavesReflected waves can interfere due to path length differences, but they can also interfere due to phase changes upon reflection.
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28-3 Interference in Reflected WavesInterference can also occur when light refracts and reflects from both surfaces of a thin film…
•Accounts for the colors we see in oil slicks and soap bubbles.
• 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.
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28-3 Interference in Reflected WavesWavelength 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:
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28-3 Interference in Reflected WavesThe condition for constructive interference:
The rainbow of colors we see is due to the different wavelengths of light.
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28-4 Diffraction
• A wave passing through a small opening will diffract, as shown.
• Means that, after the opening, there are waves traveling in directions other than the direction of the original wave.
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28-4 Diffraction
• Diffraction is why we can hear sound even though we are not in a straight line from the source….
- Sound waves will diffract around doors, corners, and other barriers.
• Amount of diffraction depends on the wavelength, which is why we can hear around corners but not see around them.
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28-4 Diffraction
• 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.
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28-4 DiffractionThis pattern is due to the difference in path length from different parts of the opening.
The first dark fringe occurs when:
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28-4 Diffraction
• 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.
• Diffraction fringes can be observed by holding your finger and thumb very close together (it helps not to be too farsighted!)
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28-5 Resolution
• Diffraction through a small circular aperture results in a circular pattern of fringes..
• 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 Diameter of aperture
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28-5 Resolution
Rayleigh’s law (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.”
Aperture with D…
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28-5 ResolutionOn the left, there appears to be a single source; on the right, two sources can be clearly resolved.
First dark fringes overlap First dark fringes don’t overlap
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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:
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28-6 Diffraction Gratings
• The positions of the peaks are different for different wavelengths of light.
• The condition for constructive interference in a diffraction grating:
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28-6 Diffraction Gratings
X-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:
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28-6 Diffraction Gratings• 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.
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Answer: The resolution of an optical instrument is greater if the minimum angular separation θ is smaller.
The minimum angle θ decreases if the wavelength decreases. Therefore, greater resolution is obtained with the blue light….