Chapter 22 Wave Optics Chapter Goal: To understand and apply the wave model of light. © 2013 Pearson Education, Inc. Slide 22-2 © 2013 Pearson Education, Inc. Models of Light . The wave model: Under many circumstances, light exhibits the same behavior as sound or water waves. The study of light as a wave is called wave optics. The ray model: The properties of prisms, mirrors, and lenses are best understood in terms of light rays. The ray model is the basis of ray optics. Chapter 23 . The photon model: In the quantum world, light behaves like neither a wave nor a particle. Instead, light consists of photons that have both wave-like and particle-like properties. This is the quantum theory of light. Physics 43 © 2013 Pearson Education, Inc. Slide 22-29 Diffraction depends on SLIT WIDTH: the smaller the width, relative to wavelength, the more bending and diffraction. Ray Optics: Ignores Diffraction and Interference of waves! Diffraction depends on SLIT WIDTH: the smaller the width, relative to wavelength, the more bending and diffraction. Ray Optics assumes that λ<<d , where d is the diameter of the opening. This approximation is good for the study of mirrors, lenses, prisms, etc. Wave Optics assumes that λ~d , where d is the diameter of the opening. d>1mm: This approximation is good for the study of interference. Geometric RAY Optics (Ch 23) nn1sin 1 2 sin 2 ir James Clerk Maxwell 1860s Light is wave. Speed of Light in a vacuum: 1 8 186,000 miles per second c3.0 x 10 m / s 300,000 kilometers per second 0 o 3 x 10^8 m/s Intensity of Light Waves E = Emax cos (kx – ωt) B = Bmax cos (kx – ωt) E ωE max c Bmax k B E B E22 c B I S maxmax max max 2 av 2μ 2 μ c 2 μ o o o I E m ax The Electromagnetic Spectrum Visible Light • Different wavelengths correspond to different colors • The range is from red (λ ~ 7 x 10-7 m) to violet (λ ~4 x 10-7 m) Limits of Vision Electron Waves 11 e 2.4xm 10 Interference of Light Wave Optics Double Slit is VERY IMPORTANT because it is evidence of waves. Only waves interfere like this. If light were made of hard bullets, there would be no interference pattern. In reality, light does show an interference pattern. Photons Light acts like a wave going through the slits but arrive at the detector like a particle. Particle Wave Duality Photons & Electrons! Interference pattern builds one electron at a time. 11 e 2.4xm 10 Electrons act like waves going through the slits but arrive at the detector like a particle. Double Slit for Electrons shows Wave Interference! Key to Quantum Theory! Electron Diffraction with Crystals Electron Microscope Electron microscope picture of a fly. The resolving power of an optical lens depends on the wavelength of the light used. An electron-microscope exploits the wave-like properties of particles to reveal details that would be impossible to see with visible light. Intereference of 2-D Coherent Light Waves RECALL: Intereference of 2-D Coherent Sound Waves Quiet Min Loud Max Quiet Min Loud Max 2 Phase Difference at P: r, 0 0 Intereference of 2-D Coherent Light Waves Young’s Double Slit • To observe interference in light waves, the following two conditions must be met: 1) The sources must be coherent • They must maintain a constant phase with respect to each other 2) The sources should be monochromatic • Monochromatic means they have a single wavelength 2 Phase Difference at P: r Constructive : 2m , r m , m 0,1,2,3... 1 Destructive : (2m 1) , r ( m ), m 0,1,2,3... 2 Fig. 37-3, p. 1086 2 Phase Difference at P: r Constructive : 2m , r m , m 0,1,2,3... 1 Destructive : (2m 1) , r ( m ), m 0,1,2,3... 2 Fig. 37-5, p. 1087 Fringe Equations “m” is the fringe order. • Maxima: bright fringes d sin θ mλ λL y m( m 0,, 1 2 ) bright d • Minima: dark fringes 1 d sin θ m λ 2 λL 1 ydark m ( m 0,, 1 2 ) d 2 Problem Red light (=664nm) is used in Young’s double slit as shown. Find the distance y on the screen between the central bright fringe and the third order bright fringe. λL y m( m 0,, 1 2 ) bright d Measuring the wavelength of light λL y m( m 0,, 1 2 ) bright d A double-slit interference pattern is observed on a screen 1.0 m behind two slits spaced 0.30 mm apart. 9 bright fringes span a distance of 1.7cm. What is the wavelength of light? L y Fringe Spacing. d Double Slit λL ybright m( m 0,, 1 2 ) The image showsd the light intensity on a screen behind a double slit. The slit spacing is 0.20 mm and the wavelength of light is 600 nm. What is the distance from the slits to the screen? Double Slit Interference Dependence on Slit Separation λL y m( m 0,, 1 2 ) bright d QuickCheck 22.5 A laboratory experiment produces a double-slit interference pattern on a screen. If green light is used, with everything else the same, the bright fringes will be λL ybright m( m 0,, 1 2 ) A. Closer together d B. In the same positions. C. Farther apart. D. There will be no fringes because the conditions for interference won’t be satisfied. Slide 22-44 QuickCheck 22.5 A laboratory experiment produces a double-slit interference pattern on a screen. If green light is used, with everything else the same, the bright fringes will be λL ybright m( m 0,, 1 2 ) A. Closer together. d B. In the same positions. C. Farther apart. D. There will be no fringes because the conditions for interference won’t be satisfied. L y and green light has a shorter wavelength. d Slide 22-45 QuickCheck 22.6 A laboratory experiment produces a double-slit interference pattern on a screen. If the slits are moved closer together, the bright fringes will be λL ybright m( m 0,, 1 2 ) A. Closer together. d B. In the same positions. C. Farther apart. D. There will be no fringes because the conditions for interference won’t be satisfied. Slide 22-46 QuickCheck 22.6 A laboratory experiment produces a double-slit interference pattern on a screen. If the slits are moved closer together, the bright fringes will be λL ybright m( m 0,, 1 2 ) A. Closer together. d B. In the same positions. C. Farther apart. D. There will be no fringes because the conditions for interference won’t be satisfied. L y and d is smaller. d Slide 22-47 QuickCheck 22.3 A laboratory experiment produces a double-slit interference pattern on a screen. What is the path difference the light travels from the two slits to the point on the screen marked with a dot? λL y m( m 0,, 1 2 ) bright d A. 1.0 . B. 1.5 . C. 2.0 . D. 2.5 . E. 3.0 . Slide 22-35 QuickCheck 22.3 A laboratory experiment produces a double-slit interference pattern on a screen. What is the path difference the light travels from the two slits to the point on the screen marked with a dot? λL y m( m 0,, 1 2 ) bright d A. 1.0 . B. 1.5 . C. 2.0 . D. 2.5 . E. 3.0 . Slide 22-36 Start Using Exam 2 Equation Sheet! Fringe Equations “m” is the fringe order. • Maxima: bright fringes d sin θ mλ λL y m( m 0,, 1 2 ) bright d • Minima: dark fringes 1 d sin θ m λ 2 λL 1 ydark m ( m 0,, 1 2 ) d 2 Single Slit Interference Is called Diffraction Light interferes with itself Single Slit Diffraction Dark fringe: sin mm 1, 2, 3,... a Dark fringe:Single sin Slitmm Problem 1, 2, 3,... a A narrow slit is illuminated with sodium yellow light of wavelength 589 nm. If the central maximum extends to ±30, how wide is the slit? Width of the Central Maximum If the incident light has =690nm (red) and a = 4 x 10-6m, find the width of the central bright fringe when the screen is 0.4m away. Dark fringe: sin mm 0,1,2,3,... a yLmm tan wy 2 Dark fringe: sin m a Compare Fringe Equations for Single and Double Slits maxima:d sinθ mλ ( m 0 , 1 , 2 ) 1 minima: d sinθ m λ ( m 0 , 1 , 2 ) 2 minima: asindark m , m 1, 2, 3,... Light Intensity: Ignoring Single Slit Diffraction • The interference pattern consists of equally spaced fringes of equal intensity – it is an idealization • This result is valid only if L >> d and for small values of θ and is an approximation of the inside fringe pattern. Reality: Combined Effects Interference maximum coincides with the first diffraction minimum. Light Intensity: Ignoring Diffraction IIcos2 ( / 2) • The interference max pattern consists of 2 equally spaced Phase Difference at P: r d sinfringesθ mλ of equal intensityλL y m( m 0,, 1 2 ) bright d Recall: Sound Power The power transmitted through a closed surface by a wave is proportional to the amplitude of the wave. Intensity~ Amplitude2 RECALL: Superposition of Sinusoidal Waves • Assume two waves are traveling in the same direction, with the same frequency, wavelength and amplitude • The waves differ in phase • y1 = A sin (kx - wt) • y2 = A sin (kx - wt + ) • y = y1+y2 = 2A cos (/2) sin (kx - wt + /2) Resultant Amplitude Depends on phase: Spatial Interference Term Intensity Distribution Resultant Field • The magnitude of the resultant electric field comes from the superposition principle – EP = E1+ E2 = Eo[sin ωt + sin (ωt + φ)] • This can also be expressed as φφ EEPo2 cos sin ωt 22 – EP has the same frequency as the light at the slits – The amplitude at P is given by 2Eo cos (φ / 2) • Intensity is proportional to the square of the amplitude: 2 2 2 φ • The maximum intensity at P IEEP P4 o cos 2 is 4 times one source!!!!!!!!! Amplitude is twice as big But intensity is proportional to the amplitude SQUARED so the Intensity is four times as big as the source.