Diffraction
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Transcript of Diffraction
24.6 Diffraction24.6 Diffraction Huygen’s principle Huygen’s principle
requires that the requires that the waves spread out after waves spread out after they pass through slitsthey pass through slits
This spreading out of This spreading out of light from its initial line light from its initial line of travel is called of travel is called diffractiondiffraction In general, diffraction In general, diffraction
occurs when wave pass occurs when wave pass through small openings, through small openings, around obstacles or by around obstacles or by sharp edgessharp edges
Diffraction, 2Diffraction, 2
A single slit placed between a distant A single slit placed between a distant light source and a screen produces a light source and a screen produces a diffraction patterndiffraction pattern It will have a broad, intense central bandIt will have a broad, intense central band The central band will be flanked by a The central band will be flanked by a
series of narrower, less intense series of narrower, less intense secondary bandssecondary bands
Called secondary maximaCalled secondary maxima The central band will also be flanked by The central band will also be flanked by
a series of dark bandsa series of dark bands Called minimaCalled minima
Diffraction, 3Diffraction, 3 The results of the The results of the
single slitsingle slit cannot cannot be explained by be explained by geometrical opticsgeometrical optics Geometrical optics Geometrical optics
would say that would say that light rays traveling light rays traveling in straight lines in straight lines should cast a should cast a sharp image of the sharp image of the slit on the screenslit on the screen
Fresnel and Fraunhofer Fresnel and Fraunhofer DiffractionDiffraction
Relation of Fresnel diffraction to Fraunhofer Relation of Fresnel diffraction to Fraunhofer diffraction by a single slitdiffraction by a single slit
Fresnel Fraunhofer
Parallel rays
Fraunhofer DiffractionFraunhofer Diffraction
Fraunhofer Fraunhofer DiffractionDiffraction occurs occurs when the rays leave when the rays leave the diffracting object the diffracting object in parallel directionsin parallel directions
A bright fringe is A bright fringe is seen along the axis seen along the axis ((θθ = 0) with = 0) with alternating bright alternating bright and dark fringes on and dark fringes on each sideeach side
24.7 Single Slit 24.7 Single Slit DiffractionDiffraction
According to Huygen’s According to Huygen’s principle, each portion of principle, each portion of the slit acts as a source of the slit acts as a source of waveswaves
The light from one portion The light from one portion of the slit can interfere of the slit can interfere with light from another with light from another portionportion
The resultant intensity on The resultant intensity on the screen depends on the the screen depends on the direction direction θθ
Single Slit Diffraction, 2Single Slit Diffraction, 2 All the waves that originate at the slit are in All the waves that originate at the slit are in
phasephase Wave 1 travels farther than wave 3 by an Wave 1 travels farther than wave 3 by an
amount equal to the path difference (amount equal to the path difference (aa/2)sin/2)sinθθ If this path difference is exactly half of a If this path difference is exactly half of a
wavelength (180wavelength (180oo), the two waves cancel each ), the two waves cancel each other and destructive interference resultsother and destructive interference results
(a/2)sin(a/2)sinθ =θ = λ/2 (for first or n = 1) or a sin θ=λλ/2 (for first or n = 1) or a sin θ=λ In general, In general, destructive interferencedestructive interference occurs for occurs for
a single slit of width a single slit of width aa when when sinsinθθdarkdark==nλnλ / /aa nn = = 1, 1, 2, 2, 3, … 3, …
Single Slit Diffraction, 3Single Slit Diffraction, 3 The general features of The general features of
the intensity distribution the intensity distribution are shownare shown
A broad central bright A broad central bright fringe is flanked by much fringe is flanked by much weaker bright fringes weaker bright fringes alternating with dark alternating with dark fringesfringes
The points of constructive The points of constructive interference lie interference lie approximately halfway approximately halfway between the dark fringesbetween the dark fringes
QUICK QUIZ 24.1
In a single-slit diffraction experiment, as the width of the slit is made smaller, the width of the central maximum of the diffraction pattern becomes (a) smaller, (b) larger, or (c) remains the same.
24.8 Diffraction Grating24.8 Diffraction Grating
The diffracting grating consists of The diffracting grating consists of many equally spaced parallel slitsmany equally spaced parallel slits A typical grating contains several A typical grating contains several
thousand lines per centimeterthousand lines per centimeter The intensity of the pattern on the The intensity of the pattern on the
screen is the result of the screen is the result of the combined effects of interference combined effects of interference and diffractionand diffraction
Diffraction Grating, cont.Diffraction Grating, cont. The condition for The condition for maximamaxima is is
d d sinsinθθbrightbright==mλmλmm=0, 1, 2, …=0, 1, 2, …
The integer The integer mm is the is the order order numbernumber of the diffraction of the diffraction patternpattern
If the incident radiation If the incident radiation contains several wavelengths, contains several wavelengths, each wavelength deviates each wavelength deviates through a specific anglethrough a specific angle
Diffraction Grating, cont.Diffraction Grating, cont. All the wavelengths are All the wavelengths are
focused at focused at mm = 0 = 0 This is called the zeroth- order This is called the zeroth- order
maximummaximum The first order maximum The first order maximum
corresponds to corresponds to mm = 1 = 1 Note the sharpness of the Note the sharpness of the
principle maxima and the principle maxima and the broad range of the dark broad range of the dark areaarea This is in contrast to to the This is in contrast to to the
broad, bright fringes broad, bright fringes characteristic of the two-slit characteristic of the two-slit interference patterninterference pattern
Grating spectrometerGrating spectrometer
The light to be The light to be analyzed passes analyzed passes through a slit and is through a slit and is formed into a parallel formed into a parallel beam by a lens. The beam by a lens. The diffracted light leaves diffracted light leaves the grating at angles the grating at angles that satisfy that satisfy d d sinsinθθbrightbright==mλmλ
Diffraction Grating in CD Diffraction Grating in CD TrackingTracking A diffraction grating A diffraction grating
can be used in a three-can be used in a three-beam method to keep beam method to keep the beam on a CD on the beam on a CD on tracktrack
The central maximum The central maximum of the diffraction of the diffraction pattern is used to read pattern is used to read the information on the the information on the CDCD
The two first-order The two first-order maxima are used for maxima are used for steeringsteering