Physics 4C. Chapter 36: Diffraction. Diffraction. Diffraction. Diffraction

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$Physics 4C Diffraction Chapter 36: Diffraction Slide 1 Slide 2 Slide 3 Slide 4 Slide 5 Slide 6 Slide 7 Slide 8 Slide 9 Slide 10 Slide 11 Slide 12 Slide 13 Slide 14 Slide 15 Slide 16 Slide 17 Slide 18$ $In an attempt to disprove the wave nature of light, in 1819 the French Academy of Sciences organized an essay competition on diffraction.$

1 Physics 4C Diffraction Chapter 36: Diffraction Slide 1 Slide 2 Slide 3 Slide 4 Slide 5 Slide 6 Slide 7 Slide 8 Slide 9 Slide 10 Slide 11 Slide 12 Slide 13 Slide 14 Slide 15 Slide 16 Slide 17 Slide 18 Slide 19 Slide 20 Slide 21 Slide 22 Slide 23 Slide 24 Slide 25 Slide 26 Slide 27 Slide 28 Slide 29 Slide 30 Slide 31 Diffraction Even though Young s double-slit experiment in 1801 provided convincing evidence for the wave nature of light, it was very slow in being adopted. In an attempt to disprove the wave nature of light, in 1819 the French Academy of Sciences organized an essay competition on diffraction. Augustin Fresnel won the competition, but most scientists did not believe his theories. Diffraction Poisson pointed out that if light truly behaved as a wave, then light waves should diffract around the edges of a sphere. If this happened, then there should be a bright spot at the center of the shadow of the sphere. The bright spot would occur because the light diffracting around the edges of the sphere should travel the same distance to the center of the shadow and produce constructive interference. 1

$The Fresnel Bright Spot Diffraction The prize committee organized a test of$ $no diffraction with diffraction Light waves from different points within a$ $interference and produce a diffraction pattern of bright and dark fringes.$ $Interference in Single-Slit Diffraction Interference in Single-Slit Diffraction$

2 The Fresnel Bright Spot Diffraction The prize committee organized a test of this prediction and discovered the predicted Fresnel bright spot. no diffraction with diffraction Light waves from different points within a single slit travel different distances in reaching a screen. Because of this, waves from different points within the slit undergo interference and produce a diffraction pattern of bright and dark fringes. Interference in Single-Slit Diffraction Interference in Single-Slit Diffraction sinα I( θ ) = Im α π a α = sinθ λ The spacing and relative intensities of the maxima and minima depend upon the values of a and λ. 2 2

$Interference in Single-Slit Diffraction$ by a Double Slit intensity from doubleslit

$intensity from diffraction of a single$ double-slit interference with slits of

3 Interference in Single-Slit Diffraction Interference in Single-Slit Diffraction Diffraction by a Double Slit Diffraction by a Double Slit intensity from doubleslit interference with vanishingly narrow slits intensity from diffraction of a single slit with width a = 5λ intensity from double-slit interference with slits of width a = 5λ 3

$Single-Slit and Double-Slit Diffraction Multiple-Slit Diffraction 3 Slits 5 Slits In double-slit interference (double-slit diffraction), the diffraction pattern from either slit acts$ $Diffraction Gratings A diffraction grating is just a very large number (1000 s) of equally spaced parallel slits (rulings).$ $The maxima (bright fringes) produced by a diffraction grating are extremely narrow and are usually called lines instead of fringes.$

4 Single-Slit and Double-Slit Diffraction Multiple-Slit Diffraction 3 Slits 5 Slits In double-slit interference (double-slit diffraction), the diffraction pattern from either slit acts like an envelope that limits the intensity of the bright fringes from the double-slit interference pattern (double-slit diffraction). As the number of slits is increased, the primary bright fringes becomes narrower and dim secondary fringes appear between each primary bright fringe. Diffraction Gratings A diffraction grating is just a very large number (1000 s) of equally spaced parallel slits (rulings). The maxima (bright fringes) produced by a diffraction grating are extremely narrow and are usually called lines instead of fringes. Diffraction Gratings Diffraction grating are incredibly useful (especially in astronomy) because the can be used to accurately measure the wavelength of light. The secondary maxima that would be between each primary maxima (line) are too dim to be seen. From d sin(θ) = mλ, you can get the wavelength of light by measuring the angular separation (θ) of the lines: λ = d sin(θ) / m 4

$Diffraction Gratings Accurately measuring the wavelength of light is$ $Diffraction Gratings By accurately measuring the wavelengths of$ light emitted by a star (or galaxy), astronomers can tell what the

light emitted by a star (or galaxy), astronomers can tell what the

$Hydrogen Helium Carbon How well a diffraction grating can resolve$ $Diffraction from Circular Aperture Diffraction from Circular$

5 Diffraction Gratings Accurately measuring the wavelength of light is important because every element (H, He, C, ) can only emit light of very specific wavelengths. Diffraction Gratings By accurately measuring the wavelengths of light emitted by a star (or galaxy), astronomers can tell what the star is made of. Hydrogen Helium Carbon How well a diffraction grating can resolve lines at different wavelengths depends upon the width of the lines. Diffraction from Circular Aperture Diffraction from Circular Aperture When light passes through a circular aperture such as a lens or the pupil of the eye, it undergoes diffraction and produces a diffraction pattern (interference pattern). 5

$Diffraction from Circular Aperture Because of$ point sources can be and still be resolved as

$Diffraction from Circular Aperture Two point$ $central maximum from one diffraction pattern$

6 Diffraction from Circular Aperture Because of diffraction, there is a limit to how close two point sources can be and still be resolved as separate. Diffraction from Circular Aperture Two point sources can barely be resolved as separate if the central maximum from one diffraction pattern overlaps the first minimum from the other. barely resolved Diffraction from Circular Aperture Pointillism 6

$Pointillism Pointillism X-Ray Diffraction For a diffraction grating, the location of the maxima are given by d sin θ = mλ or θ = sin -1 (mλ/d).$ $X-Ray Diffraction In 1912, it occurred to a physicist named Max von Laue that you could use the regular array of atoms in a crystalline solid such as sodium chloride (NaCl)$

7 Pointillism Pointillism X-Ray Diffraction For a diffraction grating, the location of the maxima are given by d sin θ = mλ or θ = sin -1 (mλ/d). For a standard diffraction grating, the slit separation is too big (d m) to resolve very small wavelengths such as x-rays (λ m). X-Ray Diffraction In 1912, it occurred to a physicist named Max von Laue that you could use the regular array of atoms in a crystalline solid such as sodium chloride (NaCl) as a kind of three-dimensional diffraction grating. The the first order maximum using x-rays occurs at: θ = sin -1 [(1)( m) /( m)] = rad = o This is too close to the central maximum to be practical. 7

$X-Ray Diffraction Most x-rays pass straight through the crystal without interacting.$ $X-Ray Diffraction The atoms in a crystal lie in various planes. Light rays can reflect off of two different planes of the crystal.$ farther than light rays reflecting off of the upper plane.

farther than light rays reflecting off of the upper plane.

8 X-Ray Diffraction Most x-rays pass straight through the crystal without interacting. However, some x-rays are scattered and form an interference pattern that is related to the atomic arrangement of the crystal. X-Ray Diffraction The atoms in a crystal lie in various planes. Light rays can reflect off of two different planes of the crystal. X-Ray Diffraction Bragg s Law for X-ray Diffraction Light rays reflecting off of the lower plane travel a distance of ΔL = 2d sin θ farther than light rays reflecting off of the upper plane. The two light rays will contructively interfere if ΔL = 2d sin θ = λ, 2λ, 3λ, The condition for constructive interference from x-ray diffraction is: 2d sin θ = m λ m = 1, 2, 3, d is the spacing between the planes (interplanar spacing) θ is the angle between the light ray and the atomic plane 8

Physics 4. Diffraction. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

$Physics 4. Diffraction. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB$ Physics 4 Diffraction Diffraction When light encounters an obstacle it will exhibit diffraction effects as the light bends around the object or passes through a narrow opening. Notice the alternating bright