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Chapter 9 Light as a Wave. 24.1 Interference Light waves interfere with each other much like mechanical waves do Light waves interfere with each other.

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Presentation on theme: "Chapter 9 Light as a Wave. 24.1 Interference Light waves interfere with each other much like mechanical waves do Light waves interfere with each other."— Presentation transcript:

1 Chapter 9 Light as a Wave

2 24.1 Interference Light waves interfere with each other much like mechanical waves do Light waves interfere with each other much like mechanical waves do All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine LINEAR SUPERPOSITION! LINEAR SUPERPOSITION!

3 Conditions for Interference For sustained interference between two sources of light to be observed, there are two conditions which must be met For sustained interference between two sources of light to be observed, there are two conditions which must be met The sources must be coherent The sources must be coherent They must maintain a constant phase with respect to each other They must maintain a constant phase with respect to each other The waves must have identical wavelengths The waves must have identical wavelengths

4 Producing Coherent Sources Light from a monochromatic source is allowed to pass through a narrow slit Light from a monochromatic source is allowed to pass through a narrow slit The light from the single slit is allowed to fall on a screen containing two narrow slits The light from the single slit is allowed to fall on a screen containing two narrow slits The first slit is needed to insure the light comes from a tiny region of the source which is coherent The first slit is needed to insure the light comes from a tiny region of the source which is coherent Old method Old method

5 Producing Coherent Sources, cont. Currently, it is much more common to use a laser as a coherent source Currently, it is much more common to use a laser as a coherent source The laser produces an intense, coherent, monochromatic parallel beam over a width of several millimeters The laser produces an intense, coherent, monochromatic parallel beam over a width of several millimeters

6 24.2 Youngs Double Slit Experiment Thomas Young first demonstrated interference in light waves from two sources in 1801 Thomas Young first demonstrated interference in light waves from two sources in 1801 Light is incident on a screen with a narrow slit, S o Light is incident on a screen with a narrow slit, S o The light waves emerging from this slit arrive at a second screen that contains two narrow, parallel slits, S 1 and S 2 The light waves emerging from this slit arrive at a second screen that contains two narrow, parallel slits, S 1 and S 2

7 Youngs Double Slit Experiment, Diagram The narrow slits, S 1 and S 2 act as sources of waves The narrow slits, S 1 and S 2 act as sources of waves The waves emerging from the slits originate from the same wave front and therefore are always in phase The waves emerging from the slits originate from the same wave front and therefore are always in phase

8 Resulting Interference Pattern The light from the two slits form a visible pattern on a screen The light from the two slits form a visible pattern on a screen The pattern consists of a series of bright and dark parallel bands called fringes The pattern consists of a series of bright and dark parallel bands called fringes Constructive interference occurs where a bright fringe occurs Constructive interference occurs where a bright fringe occurs Destructive interference results in a dark fringe Destructive interference results in a dark fringe

9 Interference Patterns Constructive interference occurs at the center point Constructive interference occurs at the center point The two waves travel the same distance The two waves travel the same distance Therefore, they arrive in phase Therefore, they arrive in phase

10 Interference Patterns, 2 The upper wave has to travel farther than the lower wave The upper wave has to travel farther than the lower wave The upper wave travels one wavelength farther The upper wave travels one wavelength farther Therefore, the waves arrive in phase Therefore, the waves arrive in phase A bright fringe occurs A bright fringe occurs

11 Interference Patterns, 3 The upper wave travels one-half of a wavelength farther than the lower wave The upper wave travels one-half of a wavelength farther than the lower wave The trough of the bottom wave overlaps the crest of the upper wave (180 phase shift) The trough of the bottom wave overlaps the crest of the upper wave (180 phase shift) This is destructive interference This is destructive interference A dark fringe occurs A dark fringe occurs

12 Interference Equations The path difference, δ, is found from the tan triangle The path difference, δ, is found from the tan triangle δ = r 2 – r 1 = |PS 2 – PS 1 | d sin θ δ = r 2 – r 1 = |PS 2 – PS 1 | d sin θ

13 Interference Equations, 2 This assumes the paths are parallel This assumes the paths are parallel Not exactly, but a very good approximation (L>>d) Not exactly, but a very good approximation (L>>d)

14 Interference Equations, 3 For a bright fringe, produced by constructive interference, the path difference must be either zero or some integral multiple of of the wavelength For a bright fringe, produced by constructive interference, the path difference must be either zero or some integral multiple of of the wavelength δ = d sin θ bright = m λ δ = d sin θ bright = m λ m = 0, ±1, ±2, … m = 0, ±1, ±2, … m is called the order number m is called the order number When m = 0, it is the zeroth order maximum When m = 0, it is the zeroth order maximum When m = ±1, it is called the first order maximum When m = ±1, it is called the first order maximum

15 Interference Equations, 4 When destructive interference occurs, a dark fringe is observed When destructive interference occurs, a dark fringe is observed This needs a path difference of an odd half wavelength This needs a path difference of an odd half wavelength δ = d sin θ dark = (n - ½) λ δ = d sin θ dark = (n - ½) λ n = ±1, ±2, … n = ±1, ±2, …

16 Interference Equations, 5 The positions of the fringes can be measured vertically from the zeroth order maximum The positions of the fringes can be measured vertically from the zeroth order maximum x = L tan θ L sin θ x = L tan θ L sin θ Assumptions Assumptions L>>d L>>d d>>λ d>>λ tan θ sin θ tan θ sin θ θ is small and therefore the approximation tan θ sin θ can be used

17 Interference Equations, final For bright fringes (use sinθ bright =m λ /d) For bright fringes (use sinθ bright =m λ /d) For dark fringes (use sinθ dark =λ (n - ½)/d) For dark fringes (use sinθ dark =λ (n - ½)/d)

18 Interference Equations, final For distance between adjacent fringes n=1 For distance between adjacent fringes n=1 This can be rearranged to the form This can be rearranged to the form

19 Uses for Youngs Double Slit Experiment Youngs Double Slit Experiment provides a method for measuring wavelength of the light Youngs Double Slit Experiment provides a method for measuring wavelength of the light This experiment gave the wave model of light a great deal of credibility This experiment gave the wave model of light a great deal of credibility It is inconceivable that particles of light could cancel each other It is inconceivable that particles of light could cancel each other

20 24.4 Interference in Thin Films Interference effects are commonly observed in thin films Interference effects are commonly observed in thin films Examples are soap bubbles and oil on water Examples are soap bubbles and oil on water Assume the light rays are traveling in air nearly normal to the two surfaces of the film Assume the light rays are traveling in air nearly normal to the two surfaces of the film

21 Interference in Thin Films, 2 Rules to remember Rules to remember An electromagnetic wave traveling from a medium of index of refraction n 1 toward a medium of index of refraction n 2 undergoes a 180° phase change on reflection when n 2 > n 1 An electromagnetic wave traveling from a medium of index of refraction n 1 toward a medium of index of refraction n 2 undergoes a 180° phase change on reflection when n 2 > n 1 There is no phase change in the reflected wave if n 2 < n 1 There is no phase change in the reflected wave if n 2 < n 1 The wavelength of light λ n in a medium with index of refraction n is λ n = λ/n, where λ is the wavelength of light in vacuum The wavelength of light λ n in a medium with index of refraction n is λ n = λ/n, where λ is the wavelength of light in vacuum

22 Interference in Thin Films, 3 Ray 1 undergoes a phase change of 180° with respect to the incident ray Ray 1 undergoes a phase change of 180° with respect to the incident ray Ray 2, which is reflected from the lower surface, undergoes no phase change with respect to the incident wave Ray 2, which is reflected from the lower surface, undergoes no phase change with respect to the incident wave 180 phase change iiii

23 Interference in Thin Films, 4 Ray 2 also travels an additional distance of 2t before the waves recombine Ray 2 also travels an additional distance of 2t before the waves recombine For constructive interference For constructive interference 2nt = (m + ½ ) λ m = 0, 1, 2 … 2nt = (m + ½ ) λ m = 0, 1, 2 … This takes into account both the difference in optical path length for the two rays and the 180° phase change This takes into account both the difference in optical path length for the two rays and the 180° phase change For destruction interference For destruction interference 2 n t = m λ m = 0, 1, 2 … 2 n t = m λ m = 0, 1, 2 …

24 Interference in Thin Films, 5 Two factors influence interference Two factors influence interference Possible phase reversals on reflection Possible phase reversals on reflection Differences in travel distance Differences in travel distance The conditions are valid if the medium above the top surface is the same as the medium below the bottom surface The conditions are valid if the medium above the top surface is the same as the medium below the bottom surface If the thin film is between two different media, one of lower index than the film and one of higher index, the conditions for constructive and destructive interference are reversed If the thin film is between two different media, one of lower index than the film and one of higher index, the conditions for constructive and destructive interference are reversed

25 Interference in Thin Films, final To form a nonreflecting coating a thin-film on glass with a minimum film thickness of λ /(4n 1 ) is required. To form a nonreflecting coating a thin-film on glass with a minimum film thickness of λ /(4n 1 ) is required. Destructive interference when: 2t=λ/(2n 1 ) Minimum thickness for nonreflecting surfaces: t=λ/(4n 1 )

26 Newtons Rings Another method for viewing interference is to place a planoconvex lens on top of a flat glass surface Another method for viewing interference is to place a planoconvex lens on top of a flat glass surface The air film between the glass surfaces varies in thickness from zero at the point of contact to some thickness t The air film between the glass surfaces varies in thickness from zero at the point of contact to some thickness t A pattern of light and dark rings is observed A pattern of light and dark rings is observed This rings are called Newtons Rings This rings are called Newtons Rings The particle model of light could not explain the origin of the rings The particle model of light could not explain the origin of the rings Newtons Rings can be used to test optical lenses Newtons Rings can be used to test optical lenses

27 Newtons rings, cont. Ray 1 undergoes a phase change of 180 on reflection, whereas ray 2 undergoes no phase change

28 Problem Solving Strategy with Thin Films, 1 Identify the thin film causing the interference Identify the thin film causing the interference The type of interference – constructive or destructive – that occurs is determined by the phase relationship between the upper and lower surfaces The type of interference – constructive or destructive – that occurs is determined by the phase relationship between the upper and lower surfaces

29 Problem Solving with Thin Films, 2 Phase differences have two causes Phase differences have two causes differences in the distances traveled differences in the distances traveled phase changes occurring on reflection phase changes occurring on reflection Both must be considered when determining constructive or destructive interference Both must be considered when determining constructive or destructive interference The interference is constructive if the path difference is an integral multiple of λ and destructive if the path difference is an odd half multiple of λ The interference is constructive if the path difference is an integral multiple of λ and destructive if the path difference is an odd half multiple of λ The conditions are reversed if one of the waves undergoes a phase change on reflection The conditions are reversed if one of the waves undergoes a phase change on reflection

30 24.5 CDs and DVDs Data is stored digitally Data is stored digitally A series of ones and zeros read by laser light reflected from the disk A series of ones and zeros read by laser light reflected from the disk Strong reflections correspond to constructive interference Strong reflections correspond to constructive interference These reflections are chosen to represent zeros These reflections are chosen to represent zeros Weak reflections correspond to destructive interference Weak reflections correspond to destructive interference These reflections are chosen to represent ones These reflections are chosen to represent ones

31 CDs and Thin Film Interference A CD has multiple tracks A CD has multiple tracks The tracks consist of a sequence of pits of varying length formed in a reflecting information layer The tracks consist of a sequence of pits of varying length formed in a reflecting information layer The pits appear as bumps to the laser beam The pits appear as bumps to the laser beam The laser beam shines on the metallic layer through a clear plastic coating The laser beam shines on the metallic layer through a clear plastic coating

32 Reading a CD As the disk rotates, the laser reflects off the sequence of bumps and lower areas into a photodector As the disk rotates, the laser reflects off the sequence of bumps and lower areas into a photodector The photodector converts the fluctuating reflected light intensity into an electrical string of zeros and ones The photodector converts the fluctuating reflected light intensity into an electrical string of zeros and ones The pit depth is made equal to one-quarter of the wavelength of the light The pit depth is made equal to one-quarter of the wavelength of the light

33 Reading a CD, cont When the laser beam hits a rising or falling bump edge, part of the beam reflects from the top of the bump and part from the lower adjacent area When the laser beam hits a rising or falling bump edge, part of the beam reflects from the top of the bump and part from the lower adjacent area This ensures destructive interference and very low intensity when the reflected beams combine at the detector This ensures destructive interference and very low intensity when the reflected beams combine at the detector The bump edges are read as ones The bump edges are read as ones The flat bump tops and intervening flat plains are read as zeros The flat bump tops and intervening flat plains are read as zeros

34 DVDs DVDs use shorter wavelength lasers DVDs use shorter wavelength lasers The track separation, pit depth and minimum pit length are all smaller The track separation, pit depth and minimum pit length are all smaller Therefore, the DVD can store about 30 times more information than a CD Therefore, the DVD can store about 30 times more information than a CD Therefore the industry is very much interested in blue (semiconductor) lasers Therefore the industry is very much interested in blue (semiconductor) lasers

35 Geometrical Optics Against Wave Optics Geometrical optics Geometrical optics Particles are running along a line forming the ray Particles are running along a line forming the ray However, geometrical optics cannot explain deflection (shadows, twilight) However, geometrical optics cannot explain deflection (shadows, twilight) WAVE OPTICS CAN! WAVE OPTICS CAN! Deflection Diffraction Linear Superposition Interference

36 Example: Red light ( =664 nm) is used in Youngs experiment according to the drawing. Find the distance y on the screen between the central bright and the third-order bright fringe. Red light ( =664 nm) is used in Youngs experiment according to the drawing. Find the distance y on the screen between the central bright and the third-order bright fringe.

37 Solution: y=Ltan =(2.75 m)(tan0.95 )=0.046 m

38 24.3 Lloyds Mirror An arrangement for producing an interference pattern with a single light source An arrangement for producing an interference pattern with a single light source Wave reach point P either by a direct path or by reflection Wave reach point P either by a direct path or by reflection The reflected ray can be treated as a ray from the source S behind the mirror The reflected ray can be treated as a ray from the source S behind the mirror

39 Interference Pattern from Lloyds Mirror An interference pattern is formed An interference pattern is formed The positions of the dark and bright fringes are reversed relative to pattern of two real sources The positions of the dark and bright fringes are reversed relative to pattern of two real sources This is because there is a 180° phase change produced by the reflection This is because there is a 180° phase change produced by the reflection

40 Phase Changes Due To Reflection An electromagnetic wave undergoes a phase change of 180° upon reflection from a medium of higher index of refraction than the one in which it was traveling An electromagnetic wave undergoes a phase change of 180° upon reflection from a medium of higher index of refraction than the one in which it was traveling Analogous to a reflected pulse on a string Analogous to a reflected pulse on a string

41 Phase Changes Due To Reflection, cont. There is no phase change when the wave is reflected from a boundary leading to a medium of lower index of refraction There is no phase change when the wave is reflected from a boundary leading to a medium of lower index of refraction Analogous to a pulse in a string reflecting from a free support Analogous to a pulse in a string reflecting from a free support


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