physics 112N interference and diffraction

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1 physics 112N interference and diffraction

2 the limits of ray optics shadow of the point of a pin physics 112N 2

3 the limits of ray optics physics 112N 3

4 the limits of ray optics physics 112N 4

5 this is how waves behave and light is an electromagnetic wave - we need to revisit wave properties physics 112N 5

6 a simple system - two wave sources suppose we have two sources emitting waves in-phase at the same frequency: S1 S2 physics 112N 6

7 the double slit experiment observe a pattern of dark and light regions, fringes physics 112N 7

8 the double slit experiment observe a pattern of dark and light regions, fringes d y R see the textbook for a derivation of bright fringes y m = m R d dark fringes y 0 m = m R d physics 112N 8

9 diffraction consider this effect seen near sharp edges: physics 112N 12

10 diffraction from a single slit shine monochromatic light onto a thin slit pattern of light and dark fringes wide central bright fringe narrower alternating dark and bright fringes decreasing intensity away from the center physics 112N 13

11 an aside on wave propagation - Huygens s principle every point of a wavefront can be considered to be a source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave t =0 wavelet after a small time source plane wavefront t = t plane wavefront physics 112N 14

12 an aside on wave propagation - Huygens s principle every point of a wavefront can be considered to be a source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave t =0 wavelet after a small time source plane wavefront t = t plane wavefront a plane wavefront begets a plane wavefront - make every point a source of secondary wavefronts physics 112N 15

13 an aside on wave propagation - Huygens s principle every point of a wavefront can be considered to be a source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave t =0 wavelet after a small time source plane wavefront t = t plane wavefront a plane wavefront begets a plane wavefront - make every point a source of secondary wavefronts plane wavefront physics 112N 16

14 an aside on wave propagation - Huygens s principle every point of a wavefront can be considered to be a source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave t =0 wavelet after a small time source plane wavefront t = t plane wavefront a plane wavefront begets a plane wavefront - make every point a source of secondary wavefronts propagated wavefront original wavefront physics 112N 17

15 an aside on wave propagation - Huygens s principle every point of a wavefront can be considered to be a source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the wave time evolution of a plane wavefront physics 112N 18

16 a single slit as many sources put the screen very far away (or use a lens) physics 112N 19

17 a single slit as many sources put the screen very far away (or use a lens) a 2 a 4... destructive interference when a 2 sin = 2 a sin 1 = destructive interference when a 4 sin = 2 a sin 2 =2... a sin m = m physics 112N 20

18 diffraction pattern from a single slit positions of dark fringes y m = m R a y 3 y 2 y 1 0 the actual intensity distribution physics 112N 21

19 diffraction and slit size positions of dark fringes y m = m R a notice that as the slit size decreases, the spreading of light increases physics 112N 22

20 a diffraction grating many slits of equal size, equally spaced angular distribution of bright fringes d sin = m physics 112N 26

21 diffraction gratings d sin = m can be used to separate different wavelengths of light in a mixed beam e.g. a beam of mixed blue and violet light : physics 112N 27

22 diffraction gratings physics 112N 28

23 a diffraction grating spectrometer d sin = m can use to make precision measurements of wavelength components useful for atomic physics... physics 112N 29

24 a diffraction grating spectrometer light from an unknown source is shone though a diffraction grating of 800 lines per mm d sin = m the diffraction pattern is observed through a rotating telescope a bright line is seen in the forward direction and rotating away from there, the next bright line is seen at 25º 25 what is the wavelength of the light? ~ 530 nm physics 112N 30

25 a diffraction grating spectrometer light from an unknown source is shone though a diffraction grating of 800 lines per mm d sin = m the diffraction pattern is observed through a rotating telescope a bright line is seen in the forward direction and rotating away from there, the next bright line is seen at 25º 25 at what angle will we see the next line? ~ 58º physics 112N 31

26 a diffraction grating spectrometer light from an unknown source is shone though a diffraction grating of 800 lines per mm d sin = m the diffraction pattern is observed through a rotating telescope a bright line is seen in the forward direction and rotating away from there, the next bright line is seen at 25º 25 when we reach 90º, how many lines will we have seen? three (including the central line) physics 112N 32

27 white light through a diffraction grating notice that the bright fringes for different colors can start to overlap can you see why this is from the equation? d sin = m physics 112N 35

28 diffraction from a circular aperture suppose the hole the light is traveling through is circular rather than a slit first dark ring is at an angle satisfying second dark ring is at an angle satisfying physics 112N 36

29 diffraction from a circular aperture e.g. the hole might be the lens of a telescope physics 112N 37

30 resolution so the ability of a telescope to resolve two objects with small angular separation is ultimately limited by the size of the lens physics 112N 38

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