Physics 1B03summer-Lecture 11 Interference of Light Light is an electromagnetic (EM) wave. Wave properties: Diffraction – bends around corners, spreads out from narrow slits Interference – waves from two or more coherent sources interfere Physics 1B03summer-Lecture 11

Electromagnetic Waves B (magnetic field) Eo v Usually we keep track of the electric field E : Electric field amplitude Electromagnetic waves are transverse waves Physics 1B03summer-Lecture 11

The Electromagnetic Spectrum l (m) f (Hz) 300 106 3 108 3 x 10-3 1011 3 x 10-6 1014 7 x 10-7 5x1014 4 x 10-7 3 x 10-9 1017 3 x 10-12 1020 Radio TV Microwave Infrared Visible Ultraviolet X rays g rays Physics 1B03summer-Lecture 11

Physics 1B03summer-Lecture 11 Infrared 780 nm Red Yellow 600 nm Green 550 nm Blue 450 nm Violet 380 nm Ultraviolet l Visible-Light Spectrum Physics 1B03summer-Lecture 11

Physics 1B03summer-Lecture 11 Interference: 2 coherent waves, out of phase due to a path difference Dr: Constructive Interference (maximum intensity) for f = 0, ±2π, ±4π, ±6π, ……… -> Δr =0, ±l, ±2 l, ±3 l, ……… Destructive Interference (minimum intensity) for f = ±π, ±3π, ±5π, ……… -> Δr =±λ/2, ±3λ/2, ±5λ/2, ……… Physics 1B03summer-Lecture 11

Physics 1B03summer-Lecture 11 Double Slit (Thomas Young, 1801) m=2 m=1 m=0 (center) m=-1 m=-2 θ incident light double slit separation d screen Result: Many bright “fringes” on screen, with dark lines in between. Physics 1B03summer-Lecture 11

Physics 1B03summer-Lecture 11 The slits act as two sources in phase. Due to diffraction, the light spreads out after it passes through each slit. When the two waves arrive at some point P on the screen, they can be in or out of phase, depending on the difference in the length of the paths. The path difference varies from place to place on the screen. P r1 To determine the locations of the bright fringes (interference maxima), we need to find the points for which the path difference Dr is equal to an integer number of wavelengths. For dark fringes (minima), the path difference is integer multiples of half of a wavelength. r2 q d Δr = r1-r2 Physics 1B03summer-Lecture 11

Physics 1B03summer-Lecture 11 For light, the slits will usually be very close together compared to the distance to the screen. So we will place the screen “at infinity” to simplify the calculation. move P to infinity r1 P r >> d, r1 & r2 nearly parallel r2 d q θ Δr = r1-r2 d θ Δr Δr = d sin θ Physics 1B03summer-Lecture 11

Physics 1B03summer-Lecture 11 Constructive Interference: (bright) Δr = mλ or d sin θ = mλ, m = 0, ±1, ±2, … But, if the slit-screen distance (L) is large, then sinθ~θ and so sinθ=θ=y/L (in radians): L y θ d So we have: Physics 1B03summer-Lecture 11

Physics 1B03summer-Lecture 11 Destructive Interference: (no light) Δr = (m + ½)λ or d sin θ = (m + ½) λ, m = 0, ±1, ±2, … So, we have: Physics 1B03summer-Lecture 11

Example y 3 m Where are a) the bright fringes? b) the dark lines? 2 slits, 0.20 mm apart; red light (l = 667 nm) y 3 m screen Where are a) the bright fringes? b) the dark lines? (give values of y) Physics 1B03summer-Lecture 11

Physics 1B03summer-Lecture 11 Concept Quiz Which of the following would cause the separation between the fringes to decrease? Increasing the wavelength Decreasing the wavelength Moving the slits closer together Moving the slits farther apart None of the above Physics 1B03summer-Lecture 11

Physics 1B03summer-Lecture 11 Concept Quiz A very thin transparent sheet placed over BOTH slits delays the waves passing through both slits by one-quarter cycle. What happens? The interference fringes disappear The fringes all shift upwards The fringes all shift downwards There is no change to the pattern. Physics 1B03summer-Lecture 11

Physics 1B03summer-Lecture 11 You want to observe interference with microwaves of frequency 10 Ghz (10 10 Hz). How far apart should you place the slits to see the pattern well? Does it matter? Physics 1B03summer-Lecture 11