sin constructive n same condition destructive 2 Interference Constructive - Destructive 2-slit single slit diff. grating

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2 Interference Constructive - Destructive 2-slit single slit diff. grating reflection Note: difference = 0 difference destructive 2 d sin reflection constructive d 2 sin tot. inter. = reflection + path length effect effect effect n same condition 8-0 n increase - /2 n decrease- no change

remember RED ORANGE YELLOW GREEN BLUE INDAGO VIOLET Prism separates light into its

3 Newton-1666 Woolsthrope Eng. White Light glass prism Contains all colors Circular Elongated ROY G BIV To help remember RED ORANGE YELLOW GREEN BLUE INDAGO VIOLET Prism separates light into its component colors [different wavelength] Before Newton it was thought that the glass darkened the white light into colors. Newton s proof of separating idea: White Light Only one color gets through. The Baroque Cycle Neal Stephenson Unusual characters!! Newton Same color: 2nd prism didn t further darken light! 8-1

5 v = wave velocity Add up 2 waves point by point Interference partial/total cancellation/increase Constructive Interference + = Destructive Interference anything in-between + = 0 8-3

light (correct) 2 wave sources interference yields large intensity

6 Corpuscular or particle theory of light 2 particle sources add in simple way (Newton believed this) Christian Huygens proposed Wave theory of light (correct) 2 wave sources interference yields large intensity oscillations Thomas Young did the experiment 1801 observed light-wave interference 8-4

7 Add 2 waves that have traveled slightly different distances. x x-x x Sum=E t x t x' 0sin(2π + 2π ) + E 0sin(2π + 2π ) T T Sum=2E 0 x - x' t [x + x'] cos(π ) sin(2π + π ) T Big difference with small x-x!! x - x' = 0,1,2,3,4...m λ cos(m ) = ±1 constructive interference x - x' = 1, 3, 5,... n λ n odd! destructive interference trig. identity time dependence same with zero shift cos(n / 2) = 0 forget time term i.e. time average squared 2 2 x - x' I =[2E 0] cos (π ) 8-5

8 + 0 - / Shifted by (+A) + (+A) =2A Constructive interference 8-5a

9 + 0 - / /2 Shifted by /2 (+A) + (-A) =0 Destructive interference 8-5b

!! new wave front old wave front Huygens point source wave fronts (maxima) propagate

10 8-6 Huygens Principle Generate how wave propagates by summing up point sources Generate all of geometrical optics!!! new wave front old wave front Huygens point source wave fronts (maxima) propagate in spherical shells Snell s law follows from wave nature of light

$http://faraday.physics.utoronto.ca/pvb/harrison/flash/waves/refraction/refraction.$

11 a

12 8-6b

13 same path length Two-Slit Experiment constructive Δ = 0, λ, 2λ,...,mλ Δ = 2λ λ Δ expanded view path length difference Δ = 0 Δ = λ 2 Δ = d sin(θ) destructive Δ = λ +λ 2 Δ = λ, λ +λ,..., λ +nλ

14 2-slit interference 8-7a

15 a-1

16 Linear Distance in an Interference Pattern H y L 2 2 tan Small angle approximation (radians) <~.1 y tan sin H y L y L y<<h or L 8-7b

17 2-slit interference demo Measure 2y ~2 cm y~.1m -9 1nm =(10) m d sin min. 2y min. 12in 2.54cm 1m L 50 ft 15.24m 1 ft 1m 100cm y y Two-Slit Interference L~ 50 ft H y sin = H 73 d~.522mm =.522(10) -3 m He-Ne 632.8nm -7 =6.33 (10) m 1 y H L sin d 2 H -7 L (15.24) 6.33(10) y m -3 2d 2(.522)(10) 92.4(10).924(10) y.924(10) y.924cm m m m expect laser small angle approx.

18 Two-Slit Interference same path length θ(first min) y Δ Δ = d sin(θ) = path length difference θ(first min) λ Δ = d sin(θ) = 2 8-8a

Two-Slit Interference min to min = 2y 28-21 homework L=1.4 m tan()=y/l=2.875 10-3 /1.4 tan()=y/l= 2.

19 Two-Slit Interference min to min = 2y homework L=1.4 m tan()=y/l= /1.4 tan()=y/l= tan()~sin() here y 23 mm = 4(2y) 8y = 23 (10) -3 m y = m y Use to find sin() d sin()=/2 d= /[2 sin()] d = /[2 ( ) ] = /4.1 (10 3 )= m 8-8b

20 Single-Slit Diffraction d 8-9

21 Single Slit Diffraction d sin 2 2 First minimum d sin a

22 a-1

$Single-Slit Diffraction d /2 sin d width d$

23 Single-Slit Diffraction d /2 sin d width d /2 d sin 2 2 sin d ~2 d Destructive 1 st 8-9b

24 Single Slit Diffraction d sin 4 2 Single-Slit Diffraction 2nd minimum 8-9c

25 8-9d Note: same trick doesn t work exactly for maxima Single-Slit Diffraction Destructive 2 nd d d /4 /4 d sin 4 2 sin 2 d d d /4 /4 Note: Higher order minima -use same argument - Divide into even number of sourced d sin 2n 2 dsin n n 1,2,3,4...

Single Slit Interference y 2 =.152/2 m = 0.076 m 28-51 632.8nm L=1.5 m tan( 2 )=y 2 /L=.076 /1.5 tan()=y/l=.

26 Single Slit Interference y 2 =.152/2 m = m nm L=1.5 m tan( 2 )=y 2 /L=.076 /1.5 tan()=y/l=.0507 tan()~sin() here 8-9e d sin1 2 2 d sin y 2 1 d sin2 4 2 d sin 2 d 2 2 sin 2(632.8) d nm.0507 d nm d m 2

27 Single slit diffraction demo laser d ~.348(10) 3 m 1 st min diff Single-Slit Diffraction He-Ne laser (10) m L H 15.24m y sin First minimum L 1 st min d sin small angle approx. d y L y 2 L 2 d y 7 (6.33)(10) m(15.24 m).348(10) 3 m 4 277(10) m 2.8 cm =3cm

28 Laser 635 mn 6.35 (10) -7 m 1 st min diff Width of Prof. Croft s Hair d sin 2 2 Hair d H y L y y sin ~ ~ L H 1 st min at y=7mm= 7(10) -3 m With L~H~1m sin d y d L L d y d d hair hair (10) 1.9(10) 7(10) 4 m -3 m m m small angle approx. 3.09(10) m.09 mm or =.1mm st min Blocking screen shape gives same pattern as hole in screen

29 d Diffraction Grating l = m Constructive interference d sin() d sin()= m λ sin(θ)=m d m = 0, 1, 2. m = 0, 1, 2. m=0 implies =0 (straight through) m>0 depends on Can use to diffract visible light from A [ A =10 cm 10 m] 8-12

30 Diffraction Grating Δ = d sin(θ) constructive Δ = 0, λ, 2λ,...,mλ white light many s different different d θ Diffraction Grating separates s Δ = d sin(θ) 8-12a

31 8-13 Diffraction Grating

32 Rules for interface reflection n >n NO PHASE CHANGE n <n PHASE CHANGE= EXTRA PATH OF /2 n n Transmission slows down n <n Reflection PHASE CHANGE= EXTRA PATH OF /2 Transmission speeds up n >n Reflection NO PHASE CHANGE 8-14

Simple effect interface reflection only interference Just before the soap film pops, it goes dark /2 phase change no phase change n>1 t If thickness t <<, then

33 Simple effect interface reflection only interference Just before the soap film pops, it goes dark /2 phase change no phase change n>1 t If thickness t <<, then 2nt/ << 2 Destructive interference for all wavelengths No reflected light Black regions t << a

34 same from this line Simple effect path length only interference mirror /2 L mirror Metal ref index~1.3 /2 change on reflection 2 L Path length difference 2 L /2 destructive interference (1 st ) 2 L constructive interference (1 st ) /2+ /2= : 2 reflections No reflection effect 2 L m m=1,2,3,4,5... constructive interference 2 L ( m 1/ 2) m=0,1,2,3,4,5... destructive interference 8-14b

35 Note: difference = 0 difference interference between rays reflected Assume incidence t Case n 2 n 3 : /2 change reflected from top & from bottom interface. PATH DIFF. IN FILM THIN FILM INTERFERENCE depends on n 1 > n 2 < n 3 n 1 n 1 < n 2 < n 3 n 1 < n 2 < n 3 : /2 change reflection changes no effect l = 2 t specify Case 1a constructive thinnest l = 2 t = n2 = / n 2 n 1 > n 2 > n 3 n 1 < n 2 > n 3... tot. inter. = reflection + path length effect effect effect figure out choose to fit Case 1b destructive thinnest l = 2 t = n2 /2 = / 2n 2 t = / 2n 2 t = / 4n Just path length gives effect

36 Example anti-reflection coating in green 532 nm n 1 < n 2 n 2 <n 3 Want /2 for destructive interference : /2 : /2 change same change have no interface reflection effect Air MnF2 glass n 1 = 1 n 2 = 1.38 n 3 = 1.50 t Want to interfere destructive (cancel) 2t tot. inter. = reflection + path length Want /2 for destructive interference must come from path length effect effect effect 0 min. thickness n2 2t 2 1 n2 t ( ) n2 2 t 1 2 n2 min 4 n 2 t min nm tmin nm 4 ( 1. 38) Note: difference = 0 difference 8-16

37 Assume incidence t interference between rays reflected n 1 =1 : /2 change n 2 =1.5 n 3 =1.33 Case n 1 < n 2 > n 3 n 1 =1 n 2 =1.5 n 3 =1.33 reflected from top & from bottom interface. no change PATH DIFF. IN FILM l = 2 t THIN FILM INTERFERENCE tot. inter. = reflection + path length effect effect effect specify figure out choose to fit /2 example Constructive enhanced reflection must undo constructive thinnest l = 2 t = n2 /2 = /2 n 2 t = / 4n 2 Reflection change : / Note: difference = 0 difference

38 Example anti-reflection coating in green 532 nm Want /2 for destructive interference n 1 < n 2 n 2 >n 3 min. thickness : /2 change no change /2 for destructive interference from reflection only Want from path length tmin nm 2 ( 1. 5) t 177 nm min Air glass water n 1 = 1 n 2 = 1.5 n 3 = 1.33 t min n 2 t Want to interfere destructive (cancel) 2t tot. inter. = reflection + path length effect effect effect Want /2 t n2 /2 2t n2 need n2 n a Note: difference = 0 difference

39 8-18

40 EM wave in vacuum f c v < c EM wave in material light slower in medium. Index of refraction: n= c / v > 1 f =c/f n AIR ICE WATER GLASS DIAMOND = v/f = /n atoms/molecules + must distort - slows propagation IM MATERIAL FREQUENCY UNCHANGED. WAVELENGTH IS SHORTER

41 8-20

Electricity & Optics

Physics 24100 Electricity & Optics Lecture 26 Chapter 33 sec. 1-4 Fall 2017 Semester Professor Koltick Interference of Light Interference phenomena are a consequence of the wave-like nature of light Electric