# Phys 2: Chap. 24, Pg 1 l Waves vs. particles l Some properties of waves: çHuygens’ principle çSuperposition — “adding” waves çCoherence l Some observed.

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Phys 2: Chap. 24, Pg 1 l Waves vs. particles l Some properties of waves: çHuygens’ principle çSuperposition — “adding” waves çCoherence l Some observed experimental effects: çInterference — double-slit experiments çDiffraction — single-slit experiments çPolarization

Phys 2: Chap. 24, Pg 2 l We observe in nature: çInterference çDiffraction çPolarization Light: Waves or Particles? l Light carries energy. But how? çAs a stream of particles travelling in the direction of the light ray? çAs a wave that spreads outward from the source? These are wave phenomena!! l In future chapters we will see light acting as a particle. çWave-particle duality

Phys 2: Chap. 24, Pg 3 Question: Suppose light falls onto a screen with two slits. What would you see on the wall behind the screen? To understand this, we must understand these principles  Huygens’ Principle  Superposition of waves  Coherence You might expect to see two bright lines on the wall: But instead you would see many lines on the wall:

Phys 2: Chap. 24, Pg 4 Huygens’ Principle All points on a wave front serve as point sources of spherical waves This also works for plane waves... Apply Huygens’ Principle to a spherical wave... Recall that a point source of light emits a spherical wave …and that far from the source, the wave is a plane wave

Phys 2: Chap. 24, Pg 5 So What? Waves can bend around corners! This is a characteristic of all waves: EM waves sound waves water waves

Phys 2: Chap. 24, Pg 6Superposition What happens when two particles are in the same place at the same time? They collide! Constructive Interference Destructive Interference + = Amplitude = 1 Amplitude = 2 What happens when two waves are in the same place at the same time? They “superpose”! Their amplitudes add to give one new wave! + = Amplitude = 1 Amplitude =  1 Amplitude = 0

Phys 2: Chap. 24, Pg 7 [wavopt1b] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless ConcepTest 1Interference ConcepTest 1(Post) Interference (1) (2) (3) (4) If waves A and B are superposed (that is, their amplitudes are added) the resultant wave is

Phys 2: Chap. 24, Pg 8 The amplitudes of waves A and B have to be added at each point! ConcepTest 1Interference ConcepTest 1(ans) Interference (1) (2) (3) (4) If waves A and B are superposed (that is, their amplitudes are added) the resultant wave is

Phys 2: Chap. 24, Pg 9Phase Phase refers to the relative position of the wave crests of the two waves Phase difference 180 o or ½ “Out of phase” Phase difference 0 o “In phase”

Phys 2: Chap. 24, Pg 10 constructive interference destructive interference waves are in phase waves are out of phase

Phys 2: Chap. 24, Pg 11Coherence Two sources of light are said to be  coherent if the phase difference between the waves emitted is always the same  incoherent if the phase difference between the waves emitted is always changing Everyday light sources are not coherent Lasers DO produce coherent light How is light produced?Oscillating electrons! For future reference: no interference patterns appear for incoherent light. In a light bulb, billions of electrons are oscillating. Is the phase difference between the light from each electron always the same? In general, NO!

Phys 2: Chap. 24, Pg 12 [wavopt2b] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless ConcepTest 2Phase ConcepTest 2(Post) Phase l The two waves shown are (1) out of phase by 180 o (2) out of phase by 90 o (3) out of phase by 45 o (4) in phase

Phys 2: Chap. 24, Pg 13 1/4 wavelength 90 o The two waves are out of phase by 1/4 wavelength (as seen in the figure), which corresponds to a phase difference of 90 o. ConcepTest 2Phase ConcepTest 2(dis) Phase l The two waves shown are (1) out of phase by 180 o (2) out of phase by 90 o (3) out of phase by 45 o (4) in phase ¼

Phys 2: Chap. 24, Pg 14 [wavopt3b] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless ConcepTest 3Phase ConcepTest 3(post) Phase (1) out of phase by 180 o (2) out of phase, but not by 180 o (3) in phase Two light sources emit waves of = 1 m which are in phase. The two waves from these sources meet at a distant point. Wave 1 traveled 2 m to reach the point, and wave 2 traveled 3 m. When the waves meet, they are

Phys 2: Chap. 24, Pg 15 one full wavelength Since = 1 m, wave 1 has traveled twice this wavelength while wave 2 has traveled three times this wavelength. Thus, their phase difference is one full wavelength which means they are still in phase. ConcepTest 3Phase ConcepTest 3(ans) Phase (1) out of phase by 180 o (2) out of phase, but not by 180 o (3) in phase Two light sources emit waves of = 1 m which are in phase. The two waves from these sources meet at a distant point. Wave 1 traveled 2 m to reach the point, and wave 2 traveled 3 m. When the waves meet, they are

Phys 2: Chap. 24, Pg 16 Interference of Sound Waves l Consider two sound waves that are in phase: çshift source by 2 wavelengths (constructive interference) 2

Phys 2: Chap. 24, Pg 17 l Now what if the shifted wave is out of phase: çshift source by 3/2 wavelengths (destructive interference) 3/2 3/2 Interference of Sound Waves

Phys 2: Chap. 24, Pg 18 Question: Suppose light falls onto a screen with two slits. What would you see on the wall behind the screen? You might expect to see two bright lines on the wall: But instead you would see many lines on the wall:

Phys 2: Chap. 24, Pg 19 l Where are the dark and bright spots and how are they related to the light’s wavelength? If both waves travel the same distance: constructive interference Explanation of the double-slit observations

Phys 2: Chap. 24, Pg 20 Explanation of the double-slit Observations We can explain the pattern of bright and dark fringes by 1. bending (diffraction / Huygens’ Principle) and2. superposition (adding of amplitudes) of 3. coherent light waves! Bottom wave travels 1 whole extra wavelength. When waves meet, they are in phase: constructive interference Bottom wave travels ½ extra wavelength. When waves meet, they are out of phase: destructive interference 1 / 2

Phys 2: Chap. 24, Pg 21 constructive destructive

Phys 2: Chap. 24, Pg 22 Double-Slit Interference: The Math Path difference  between waves determines phase difference: m is an integer: m = 0, ± 1, ± 2,...  d L y  r1r1 r2r2  = r 2 - r 1 = d sin  For Destructive Interference  = 1 / 2, 3 / 2, 5 / 2, 7 / 2, … = (m + 1 / 2 ) d sin  = (m + 1 / 2 ) For Constructive Interference  = 1, 2, 3, 4, … = m d sin  = m 

Phys 2: Chap. 24, Pg 23 Intensity of Fringes m =0112233 Constructive Interference m = Destructive Interference Light Intensity 00112233

Phys 2: Chap. 24, Pg 24 [wavopt4b] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless ConcepTest 4Interference ConcepTest 4(Post) Interference l In a double-slit experiment, when the wavelength of the light is increased, the interference pattern (1) spreads out (2) stays the same (3) shrinks together (4) disappears

Phys 2: Chap. 24, Pg 25 is increasedd does not change  must increase If is increased and d does not change, then  must increase, so the pattern spreads out. ConcepTest 4Interference ConcepTest 4(Ans) Interference l In a double-slit experiment, when the wavelength of the light is increased, the interference pattern (1) spreads out (2) stays the same (3) shrinks together (4) disappears d sin  = m  d sin  = m 

Phys 2: Chap. 24, Pg 26 [wavopt5b] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless ConcepTest 5Interference ConcepTest 5(Post) Interference (1) spreads out (2) stays the same (3) shrinks together (4) disappears l If instead the slits are moved farther apart (without changing the wavelength), the interference pattern

Phys 2: Chap. 24, Pg 27 d is increased does not change  must decrease If instead d is increased and does not change, then  must decrease, so the pattern shrinks together. ConcepTest 5Interference ConcepTest 5(Ans) Interference (1) spreads out (2) stays the same (3) shrinks together (4) disappears d sin  = m  d sin  = m  l If instead the slits are moved farther apart (without changing the wavelength), the interference pattern

Phys 2: Chap. 24, Pg 28 l Light of wavelength 680 nm falls on two slits and produces an interference pattern in which the fourth-order maximum is 48 mm from the central fringe on a screen 1.5 m away. çWhat is the separation between the two slits? Double-slit interference See Problem 24-7

Phys 2: Chap. 24, Pg 29 Double-Slit Interference Calculate the distance of the bright fringes from the axis: Note that tan  = y/L. By hypothesis, L >> y, so then tan  and thus  are both << 1. Then tan  sin  to a good approximation. So the bright fringes will be at: therefore: So the bright fringes are evenly spaced a distance L/d apart.

Phys 2: Chap. 24, Pg 30 Light of wavelength 680 nm falls on two slits and produces an interference pattern in which the fourth-order maximum is 48 mm from the central fringe on a screen 1.5 m away. What is the separation between the two slits?Problem Constructive or Destructive Interference? “maximum”  Constructive Equation for fringes? Constructive  d sin  = m Algebra d= m / sin  = m L / y Plug in numbers m= 4 = 680 nm = 680  10 –9 m L= 1.5 m y= 0.048 m d= 0.085 mm What is sin  ? L y  sin   tan  = y/L

Phys 2: Chap. 24, Pg 31 [wavop10b] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless ConcepTest 10Interference ConcepTest 10(Post) Interference l An interference pattern is seen from two slits. (1) pattern vanishes (2) pattern expands (3) bright and dark spots are interchanged (4) pattern shrinks (5) no change at all Double slit Interference pattern wave l Now cover one slit with glass, introducing a phase difference of 180° (½ wavelength) at the slits. How is the pattern altered?

Phys 2: Chap. 24, Pg 32 phase difference of 180° dark bright and dark spots are interchanged If the waves originating from the two slits have a phase difference of 180° when they start off, the central spot will now be dark. To the left and the right, there will be bright spots. Thus, bright and dark spots are interchanged. ConcepTest 10Interference ConcepTest 10(ans) Interference Double slit Interference pattern wave (1) pattern vanishes (2) pattern expands (3) bright and dark spots are interchanged (4) pattern shrinks (5) no change at all l An interference pattern is seen from two slits. l Now cover one slit with glass, introducing a phase difference of 180° (½ wavelength) at the slits. How is the pattern altered?

Phys 2: Chap. 24, Pg 33 What is Diffraction? Waves can bend around corners! This is a characteristic of all waves: EM waves sound waves water waves

Phys 2: Chap. 24, Pg 34 Diffraction What is actually seen, close to the edge of the shadow, is incident light screen

Phys 2: Chap. 24, Pg 35 Diffraction What if we shined coherent light through a single slit? But instead you would see many lines on the wall: Diffraction pattern  

Phys 2: Chap. 24, Pg 36 Single-slit diffraction l Light falls straight through the slit çforms a central bright line on the screen Now look at light falling through at angle  such that the top and bottom waves are one wavelength apart. Now look at light falling through at angle  such that the top and bottom waves are one wavelength apart. this gives destructive interference  This center wave is exactly half a wavelength    2 out of phase with this bottom wave

Phys 2: Chap. 24, Pg 37 Single-slit diffraction D    l Eventually we get following pattern: sin  =  D l The angle corresponding to the first minimum : D sin  = m Equation for all minima:

Phys 2: Chap. 24, Pg 38

Phys 2: Chap. 24, Pg 39 [wavopt7b] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless ConcepTest 7Diffraction ConcepTest 7(Post) Diffraction screen Slide with slit l The diffraction pattern below arises from a single slit. If we would like to sharpen the pattern, i.e. make the central bright spot narrower, what should we do to the slit width? (1) narrow the slit (2) widen the slit (3) enlarge the screen (4) close off the slit

Phys 2: Chap. 24, Pg 40 The angle at which the first minimum occurs is: smaller angle widening the slit The central bright spot can be made narrower by having a smaller angle, which can be accomplished by widening the slit (increasing D). ConcepTest 7Diffraction ConcepTest 7(ans) DiffractionD    sin  =  D l The diffraction pattern below arises from a single slit. If we would like to sharpen the pattern, i.e. make the central bright spot narrower, what should we do to the slit width? (1) narrow the slit (2) widen the slit (3) enlarge the screen (4) close off the slit

Phys 2: Chap. 24, Pg 41 [wavopt8b] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless ConcepTest 8Diffraction ConcepTest 8(Post) Diffraction Blue light of wavelength passes through a single slit of width d and forms a diffraction pattern on a screen. If the blue light is replaced by red light of wavelength 2, the original diffraction pattern can be reproduced if the slit width is changed to: (1) d/4 (2) d/2 (3) no change needed (4) 2 d (5) 4 d

Phys 2: Chap. 24, Pg 42 ConcepTest 8Diffraction ConcepTest 8(ans) Diffractiond    d sin  = m (minima) If  2 then we must have d  2d for sin  to remain unchanged (and thus give the same diffraction pattern). Blue light of wavelength passes through a single slit of width d and forms a diffraction pattern on a screen. If the blue light is replaced by red light of wavelength 2, the original diffraction pattern can be reproduced if the slit width is changed to: (1) d/4 (2) d/2 (3) no change needed (4) 2 d (5) 4 d

Phys 2: Chap. 24, Pg 43 l How wide is the central diffraction peak on a screen 2.50 m behind a 0.0348 mm wide slit illuminated by 589 nm light? Diffraction See Problem 24-22 D   

Phys 2: Chap. 24, Pg 44 Diffraction + Interference Wait a minute! If we have two slits, don’t we also get a diffraction pattern from each slit, in addition to the interference pattern? If another slit is opened adjacent to the first, the pattern now has an interference pattern: If laser light illuminates one slit: diffraction minimum interference minimum

Phys 2: Chap. 24, Pg 45 Intensity of Fringes m =0112233 Constructive Interference m = Destructive Interference Light Intensity 00112233

Phys 2: Chap. 24, Pg 46 Diffraction Grating l A large number of equally spaced slits (up to 10,000 !) is called a diffraction grating çuseful for measuring wavelengths çwhat does the interference pattern look like? l Similar to the 2-slit situation, but peaks are much narrower.

Phys 2: Chap. 24, Pg 47 l Assume that the light striking a diffraction grating has several wavelengths (it is not monochromatic). l Remember that white light contains all the colors of the s p e c t r u m The Visible Spectrum each color in the spectrum has a different wavelength

Phys 2: Chap. 24, Pg 48 Diffraction grating with different colors l If the light has two wavelengths, we get two sets of maxima: l If it is white light (all colors, therefore all wavelengths):

Phys 2: Chap. 24, Pg 49 Interference by Thin Films l Example -- thin oil film on water: çPart of the incoming light is reflected off the top surface (point A), part at the lower surface (point B). çLight traveling through oil travels extra distance (from A to B to C).  If this distance is  2  3  4  … »constructive interference!  If this distance is  2  3  2  5  2  … »destructive interference!

Phys 2: Chap. 24, Pg 50 Newton’s Rings l More interference: air gap between two pieces of glass. çPath difference increases for the wave reflected at bottom surface (point C).  If the extra path length is  2  3  4  … »constructive interference!  If the extra path length is  2  3  2  5  2  … »destructive interference!

Phys 2: Chap. 24, Pg 51 ConcepTest 11Interference ConcepTest 11(Pre) Interference [wavop11a] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless l A laser shines on a pair of identical glass microscope slides that form a very narrow edge. The waves reflected from the top and the bottom slide interfere. What is the interference pattern from top view? edge (1) (2)

Phys 2: Chap. 24, Pg 52 no phase difference constructively changes phase by  2 Right at the edge, the two reflected rays have no phase difference and therefore should interfere constructively. However, the light ray reflected at the lower surface (point E) changes phase by  2 because the index of refraction of glass is larger than that of air. ConcepTest 11Interference ConcepTest 11(ans) Interferenceedge (1) (2) l A laser shines on a pair of identical glass microscope slides that form a very narrow edge. The waves reflected from the top and the bottom slide interfere. What is the interference pattern from top view?

Phys 2: Chap. 24, Pg 53 Reflection of waves on surfaces If a light wave is reflected by a material whose index of refraction is greater than that of the material it is going through, the wave changes phase by  2  If a light wave is reflected by a material whose index of refraction is greater than that of the material it is going through, the wave changes phase by  2  çexample: air and oil, oil and water, etc. l This is similar to a wave pulse traveling on a rope and being reflected with the end tied down. çThe pulse flips over  the wave changes phase.

Phys 2: Chap. 24, Pg 54 And the other way around... l If a light wave is reflected by a material whose index of refraction is less than that of the material it is going through, there is no phase change. l This is similar to a wave pulse traveling on a rope and being reflected with the end loose. çThe pulse travels back the same way it came  no phase change.

Phys 2: Chap. 24, Pg 55 [wavop12b] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless ConcepTest 12Interference ConcepTest 12(post) Interference l Consider two identical microscopic slides in air illuminated with light from a laser. The bottom slide is rotated upwards so that the wedge angle gets a bit smaller. What happens to the interference fringes? (1) Spaced farther apart (2) Spaced closer together (3) No change

Phys 2: Chap. 24, Pg 56 The path difference between Ray #2 and Ray #3 is 2t. Ray #3 also experiences a phase change of 180°. Thus, the dark fringes will occur for: 2t = m m = 0,1,2,… If t gets smaller, Ray #2 and Ray #3 have to be further apart before they can interfere. Thus, the fringes move apart. ConcepTest 12Interference ConcepTest 12(ans) Interference l Consider two identical microscopic slides in air illuminated with light from a laser. The bottom slide is rotated upwards so that the wedge angle gets a bit smaller. What happens to the interference fringes? ray 1 ray 2 ray 3 t (1) Spaced farther apart (2) Spaced closer together (3) No change

Phys 2: Chap. 24, Pg 57Polarization 1 electron E field oscillates in one direction polarized light 3-D view: The E field in an EM wave is perpendicular to the direction of travel But there are many possible orientations for the E field! millions of electrons E field oscillates in all directions unpolarized light 3-D view: In polarized light, all of the electric fields in the wave oscillate in the same direction

Phys 2: Chap. 24, Pg 58 Polarization by Absorption 1) scattering Three ways to polarize light 2) reflection 3) absorption unpolarized polarized E field of wave Wave passes through E field of wave Wave absorbed Polarization by absorption: Vertical components of wave are absorbed by antenna Horizontal components pass through polaroid long thinmolecules (light) wires (radio waves)

Phys 2: Chap. 24, Pg 59 How much light gets through? E field:E o Intensity:I o E field:? Intensity:? Intensity of the outgoing polarized light: I = I 0 cos 2 

Phys 2: Chap. 24, Pg 60 Polarization No light l First polaroid allows only one orientation of the electric field to pass, thus polarizing the light. l Second polaroid is oriented perpendicular to the first one, so no light can pass through it.

Phys 2: Chap. 24, Pg 61 [wavop14b] RESPONDEX Contro l Y 1 A 2 B 4 D 5 E 6 7 89 0 N Interactive Classroom U All Done 3 C Wireless ConcepTest 14Polarization ConcepTest 14(post) Polarization l If unpolarized light is incident from the left, in which case will some light get through? (1) only case 1 (2) only case 2 (3) only case 3 (4) cases 1 and 3 (5) all three cases

Phys 2: Chap. 24, Pg 62 ConcepTest 14Polarization ConcepTest 14(ans) Polarization l If unpolarized light is incident from the left, in which case will some light get through? (1) only case 1 (2) only case 2 (3) only case 3 (4) cases 1 and 3 (5) all three cases intermediate 45° polarizer In cases 1 and 3, light is blocked by the adjacent horizontal and vertical polarizers. In case 2, the intermediate 45° polarizer allows some light to get through the last vertical polarizer.

Phys 2: Chap. 24, Pg 63 l Two polarizers are oriented at 58° to one another. Light polarized at a 29° angle to each polarizer passes through both. çWhat reduction in intensity takes place ? Polarization See Problem 24-61

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