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Chapter 24 The Wave Nature of Light AP Physics B Mrs. Wallace Wave Optics Sections 24-01 Conditions for Interference 24-02 24-03 24-04 24-06 Young’s Double-Slit Experiment Change of Phase Due to Reflection Interference in Thin Films Diffraction 24-07 Single-Slit Diffraction 24-08 The Diffraction Grating Wave Optics 24 (02 of 41) Conditions for Interference For observable interference effects, sources must be 1. Coherent Waves must maintain a constant phase relationship 2. Monochromatic Waves must have the same wavelength Wave Optics 24 (03 of 41) Chapter 24: Wave Optics Two light sources are said to be coherent if they (A) are of the same frequency. (B) are of the same frequency, and maintain a constant phase difference. (C) are of the same amplitude, and maintain a constant phase difference. (D) are of the same frequency and amplitude. Wave Optics 24 (04 of 41) Young’s Double-Slit Experiment If light is a wave, interference effects will be seen, where one part of wavefront can interact with another part. One way to study this is to do a double-slit experiment: Wave Optics 24 (05 of 41) Young’s Double-Slit Experiment Wave Optics 24 (06 of 41) Young’s Double-Slit Experiment The interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot). Wave Optics 24 (07 of 41) Chapter 24: Wave Optics What principle is responsible for alternating light and dark bands when light passes through two or more narrow slits? (A) refraction (B) polarization (C) dispersion (D) interference Wave Optics 24 (08 of 41) Young’s Double-Slit Experiment We can use geometry to find the conditions for constructive and destructive interference: Bright (constructive interference) d sin θ mλ , m 0, 1, 2, .... Dark (destructive interference) d sin θ m 1 λ , 2 m 0, 1, 2, .... Wave Optics 24 (09 of 41) Young’s Double-Slit Experiment PS2 - PS1 = d sin(q) P S1 q d Constructive Interference S2 q d sin(θ) mλ m 0, 1, 2, . . . Destructive Interference 1 d sin(θ) m λ 2 m 0, 1, 2, . . . screen Wave Optics 24 (10 of 41) Young’s Double-Slit Experiment sin(θ) tan(θ) Bright y L y S1 d q Constructive Interference S2 L d sinθ mλ y (bright ) mLλ d m 0, 1, 2, Δy Lλ d screen Wave Optics 24 (11 of 41) Young’s Double-Slit Experiment Dark y sin(θ) tan(θ) L y S1 d q Destructive Interference S2 1 d sin(θ) m 2 m 0, 1, 2, . . . L 1 m Lλ 2 y dark d Lλ Δy d screen Wave Optics 24 (12 of 41) Chapter 24: Wave Optics In a Young's double slit experiment, if the separation between the slits decreases, what happens to the distance between the interference fringes? (A) It decreases. (B) It increases. Lλ Δy d (C) It remains the same. (D) There is not enough information to determine. Wave Optics 24 (13 of 41) Chapter 24: Wave Optics At the first minima on either side of the central bright spot in a double-slit experiment, light from each opening arrives (A) in phase. (B) 90° out of phase. (C) 180° out of phase. (D) none of the given answers Wave Optics 24 (14 of 41) Chapter 24: Wave Optics At the second maxima on either side of the central bright spot in a double-slit experiment, light from (A) each opening travels the same distance. (B) one opening travels twice as far as light from the other opening. (C) one opening travels one wavelength of light farther than light from the other opening. (D) one opening travels two wavelengths of light farther than light from the other opening. Wave Optics 24 (15 of 41) Chapter 24: Wave Optics What principle is responsible for light spreading as it passes through a narrow slit? (A) refraction (B) polarization (C) diffraction (D) interference Wave Optics 24 (28 of 41) Diffraction Wave Optics 24 (27 of 41) Single-Slit Diffraction The resulting pattern of light and dark stripes is called a diffraction pattern. This pattern arises because different points along a slit create wavelets that interfere with each other just as a double slit would. The minima of the single-slit diffraction pattern occur when D sin θ mλ m 1, 2, 3, .... Wave Optics 24 (29 of 41) Single-Slit Diffraction q d L y2 sin θ 2λ y1 sin θ λ 0 sin θ 0 y1 sin θ λ y2 sin θ 2λ d d d d Wave Optics 24 (30 of 41) Chapter 24: Wave Optics A person gazes at a very distant light source. If she now holds up two fingers, with a very small gap between them, and looks at the light source, she will see (A) the same thing as without the fingers, but dimmer. (B) a series of bright spots. (C) a sequence of closely spaced bright lines. (D) a hazy band of light varying from red at one side to blue or violet at the other. Wave Optics 24 (31 of 41) Single-Slit Diffraction A single slit of width 0.30 mm is illuminated with 650 nm light. An interference pattern is formed on a screen 2.5 m away. Find the distance from the first dark band to the central bright band. λ sin θ d λ y d L y tanθ L Lλ y d sinθ tanθ y d 2.5 m 6.5x10 7 m 3.00 x 10 4 m y 0.0054 m Wave Optics 24 (32 of 41) Single-Slit Diffraction A single slit of width 0.14 mm is illuminated by monochromatic light and interference bands are observed on a screen 2.0 m away. If the second dark band is 16 mm from the central bright band, what is the wavelength of the light? D sin θ mλ m2 2λ sin θ D y tan θ sin θ L y yD λ 2L L q D y 2λ L D 0.016 m0.00014 m 22.0 m λ 5.6 x 10 7 m 560 nm Wave Optics 24 (33 of 41) The Diffraction Grating A diffraction grating consists of a large number of equally spaced narrow slits or lines. A transmission grating has slits, while a reflection grating has lines that reflect light. Two slits The more lines or slits there are, the narrower the peaks. Six slits Wave Optics 24 (34 of 41) Chapter 24: Wave Optics Consider two diffraction gratings with the same slit separation, one grating has 3 slits and the other 4 slits. If both gratings are illuminated with a beam of the same monochromatic light, make a statement concerning the separation between the orders. (A) The grating with 3 slits produces the greater separation between orders. (B) The grating with 4 slits produces the greater separation between orders. (C) Both gratings produce the same separation between orders. (D) Both gratings produce the same separation between orders, but the orders are better defined with the 4-slit grating. Wave Optics 24 (35 of 41) The Diffraction Grating The maxima of the diffraction pattern are defined by d sin θ mλ , m 0, 1, 2, 3, ...... Wave Optics 24 (36 of 41) The Diffraction Grating (Problem) A 3500-line/cm grating produces a third-order fringe at a 28.0o angle. What is the wavelength of light being used? d sin θ mλ λ d sin θ m 1 λ 350,000 sin 28.0o lines m 3 4.47 x 10 7 m 447 nm Wave Optics 24 (37 of 41) The Diffraction Grating (Problem) A diffraction grating has 6.0 x 105 lines/m. Find the angular spread in second-order spectrum between red light of wavelength 7.0 x 107 m and blue light of wavelength 4.5 x 107 m. B qB qR R Dq d sin θ mλ m=2 2 7.0 x 10 7 m 57.1o θ R sin 1 1 5 6.0 x 10 line/m 2 4.5 x 10 7 m 32.7o θB sin 1 1 5 6.0 x 10 line/m Δθ 57.1o 32.7o 24.4o Wave Optics 24 (39 of 41) The Diffraction Grating The Spectrometer and Spectroscopy A spectrometer makes accurate measurements of wavelengths using a diffraction grating or prism. Wave Optics 24 (39 of 41) The Diffraction Grating The Spectrometer and Spectroscopy The wavelength can be determined to high accuracy by measuring the angle at which the light is diffracted. λ d sin θ m Atoms and molecules can be identified when they are in a thin gas through their characteristic emission lines. Wave Optics 24 (40 of 41) Change of Phase Due to Reflection A reflected light wave undergoes a phase change of 180o. Wave Optics 24 (16 of 41) Change of Phase Due to Reflection A reflected light wave undergoes no phase change. Wave Optics 24 (17 of 41) Chapter 24: Wave Optics When a beam of light, which is traveling in glass, strikes an air boundary, there is (A) a 90° phase change in the reflected beam. (B) a 180° phase change in the reflected beam. (C) a 45° phase change in the reflected beam. (D) no phase change in the reflected beam. Wave Optics 24 (18 of 41) Interference in Thin Films Another way path lengths can differ, and waves interfere, is if they travel through different media. If there is a very thin film of material – a few wavelengths thick – light will reflect from both the bottom and the top of the layer, causing interference. This can be seen in soap bubbles and oil slicks, for example. air 1λ 2 glass No phase change phase change air Wave Optics 24 (19 of 41) Interference in Thin Films If t t 1 λ Dark (minima) 2 t 1 λ Bright (maxima) 4 Wave Optics 24 (20 of 41) Interference in Thin Films a b t n The phase displacement of (b) relative to (a) is 1 λ Due to reflection 2 2tn Due to path difference When 12 2tn is 12 , 32 , 52 , ... m 12 When 12 2tn is , 2 , 3 , ... m There is darkness There is brightness Wave Optics 24 (21 of 41) Interference in Thin Films (Problem) A tanker has dumped a large quantity of kerosene into the gulf creating a large slick on the top of the water. You are looking straight down from an airplane onto a region of the slick where its thickness is t = 460 nm. Which wavelength of visible light is reflected the greatest? a 2tn' mλ b air n = 1.0 kerosene n’ = 1.2 water n’’ = 1.3 t 2tn' λ m 2460 nm 1.2 λ m m 1 λ 1104 nm m 2 λ 552 nm m 3 λ 368 nm Wave Optics 24 (22 of 41) Interference in Thin Films A tanker has dumped a large quantity of kerosene into the gulf creating a large slick on the top of the water. You are a scubadiver directly under the slick where its thickness is t = 460 nm. Which wavelength of visible light is the transmitted intensity the greatest? 1 λ 2tn' mλ 2 n = 1.0 air kerosene n’ = 1.2 water n’’ = 1.3 a b 2tn' λ 1 m t 2 2460 nm 1.2 λ m1 m 1 λ 2208 nm m 2 λ 736 nm m 3 λ 441 nm m 4 λ 315 nm 2 Wave Optics 24 (23 of 41) Interference in Thin Films One can also create a thin film of air by creating a wedgeshaped gap between two pieces of glass. Wave Optics 24 (24 of 41) Interference in Thin Films 1 1 Dark 2 2t m 2 m=1 m=0 D A R K t 0 B R I G H T D A R K λ t 2 m=2 B R I G H T D A R K tλ Wave Optics 24 (25 of 41) Interference in Thin Films Problem Solving: Interference Interference occurs when two or more waves arrive simultaneously at the same point in space. Constructive interference occurs when the waves are in phase. Destructive interference occurs when the waves are out of phase. An extra half-wavelength shift occurs when light reflects from a medium with higher refractive index. Wave Optics 24 (26 of 41)