Optics Wave Behavior in Optics Interference from Multiple Slits Diffraction Gratings

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1 Optics Wave Behavior in Optics Interference from Multiple Slits Diffraction Gratings Lana Sherian De Anza College June 14, 2018

2 Last time images forme by lens combinations Huygen s Principle Interference of light: the Double-Slit experiment

3 Overview Interference of light: the Double-Slit experiment multiple slit interference iffraction gratings

4 37.5b), which is approximately true if L is much greater than, then is given by Young s Experiment: Fining the Maxima 5 r 2 2 r 1 5 sin u (37.1) The value of etermines whether the two waves are in phase when they arrive at point Effectively, P. If is either the two zero rays or some areinteger parallel. multiple of the wavelength, the two waves P r 1 r 1 S 1 y S 1 r 2 Q S 2 u u r 2 u O S 2 r 2 r 1 sin u L Viewing screen When we assume r 1 is parallel to r 2, the path ifference between the two rays is r 2 r 1 sin u. a Looking at the right triangle with hypotenuse (the slit separation istance): δ = sin θ. b

5 Young s Experiment: Fining the Angles of the Maxima Maxima (bright fringes) occur when sin θ max = mλ where m Z Minima (ark fringes) occur when sin θ min = ( m + 1 ) λ 2 where m Z These expressions give us the angles (measure outwar from the axis that passes through the mipoint of the slits) where the bright an ark fringes occur.

6 Orer Number m is the orer number. The central bright fringe is the 0th orer fringe, the neighboring ones are the 1st orer fringes, etc. 1 Figure from Quantum Mechanics an the Multiverse by Thomas D. Le.

7 ence (Greek letter elta). If we assume the rays labele r 1 an r 2 ar 37.5b), which is approximately true if L is much greater than, then Young s Experiment: Fining the Position of the Maxima 5 r 2 2 r 1 5 sin u We canthe alsovalue preict of the etermines istance whether from the center two of waves the are screen, in phase y, when in terms point of the P. If istance either from zero the or slits some tointeger the screen, multiple L. of the wavelength P r r 1 S 1 y S 1 Q r 2 u u u O S 2 S 2 r 2 r 1 L tan θ = y L Viewing screen When we assum parallel to r 2, th ifference betwe rays is r 2 r 1

8 Young s Experiment: Fining the Position of the Maxima Maxima (bright fringes) occur at y max = L tan θ max Minima (ark fringes) occur at y min = L tan θ min

9 Young s Experiment: Fining the Position of the Maxima When θ is also small, sin θ tan θ, an we can use our earlier expressions for the fringe angles. Maxima (bright fringes) occur at y max = L mλ (small θ) Minima (ark fringes) occur at y min = L ( m + 1 2) λ (small θ)

10 Young s Experiment Question Quick Quiz Which of the following causes the fringes in a two-slit interference pattern to move farther apart? (A) ecreasing the wavelength of the light (B) ecreasing the screen istance L (C) ecreasing the slit spacing (D) immersing the entire apparatus in water 1 Serway & Jewett, page 1138.

11 Young s Experiment Question Quick Quiz Which of the following causes the fringes in a two-slit interference pattern to move farther apart? (A) ecreasing the wavelength of the light (B) ecreasing the screen istance L (C) ecreasing the slit spacing (D) immersing the entire apparatus in water 1 Serway & Jewett, page 1138.

12 Double-Slit Fringes of Two Wavelengths, Ex 37.2 A light source emits visible light of two wavelengths: λ = 430 nm an λ = 510 nm. The source is use in a ouble-slit interference experiment in which L = 1.50 m an = mm. Fin the separation istance between the thir-orer bright fringes for the two wavelengths.

13 Double-Slit Fringes of Two Wavelengths, Ex 37.2 A light source emits visible light of two wavelengths: λ = 430 nm an λ = 510 nm. The source is use in a ouble-slit interference experiment in which L = 1.50 m an = mm. Fin the separation istance between the thir-orer bright fringes for the two wavelengths. y = y max y max = L mλ L mλ

14 Double-Slit Fringes of Two Wavelengths, Ex 37.2 A light source emits visible light of two wavelengths: λ = 430 nm an λ = 510 nm. The source is use in a ouble-slit interference experiment in which L = 1.50 m an = mm. Fin the separation istance between the thir-orer bright fringes for the two wavelengths. y = y max y max = L mλ L mλ = L m (λ λ) = 1.44 cm

15 Young s Experiment: Intensity Distribution Consier the electric fiel at a certain point P on the screen from each slit: E 1 = E 0 sin(ωt) E 2 = E 0 sin(ωt + φ)

16 Young s Experiment: Intensity Distribution Consier the electric fiel at a certain point P on the screen from each slit: E 1 = E 0 sin(ωt) E 2 = E 0 sin(ωt + φ) Using ( ) ( ) α β α + β sin α + sin β = 2 cos sin 2 2 We see that the net E-fiel at that point P is: E P = E 1 + E [ 2 ( )] ( φ = 2E 0 cos sin ωt + φ ) 2 2 Amplitue Time-fluctuation

17 Young s Experiment: Intensity Distribution E P,max = 2E 0 cos ( ) φ 2 Relating E-fiel to intensity, recall (Ch. 34): I E 2 P,max So, ) I = I max cos 2 ( φ 2 The phase ifference is relate to δ, the path ifference by: φ 2π = δ λ So, using δ = sin θ (an φ = 2π sin θ/λ) ( ) π sin θ I = I max cos 2 λ

18 Young s Experiment: Intensity Distribution ( ) π sin θ I = I max cos 2 λ Q uick Quiz 37.2 Using Figure from six slits. N 2 N 3 N 4 I I max N 5 2l l 0 l 2l sin u N 10 2l l Figure 37.6 Light intensity versus sin u for a Figure 37.7 Mul

19 E 2 are represente by phasors φ E 0 at Young s angular Experiment: spee v. The values Intensity Distribution ω t e corresponing phasors on the ( ) their projections at an arbitrary φ E = 2E 0 cos (a) e phasor for E 2 1 has a rotation ngle UBLE-SLIT vt f (it INTERFERENCE is phase-shifte 971 n on the vertcal axis varies with ns of Eqs an vary at any E 2 point P in Fig , we β 13b.The magnitue E ω 0 of the vector E φ oint E 1 P,an that wave has a cer- E 1 Fig b,we φ first E 0 note that the β E 0 e opposite ω equal-length t sies of ωt at an exterior angle (here f, as o opposite interior angles Phasors (here ( ) that represent φ ave (a) I = I (b) max cos waves can 2 be 2 Fig. ae to (a) Phasors repres E 2 Phasors that PART waves 4 can be fin the net w E 0 ω

20 Interference with Three Slits E 1 = E 0 sin(ωt), E 2 = E 0 sin(ωt + φ), E 3 = E 0 sin(ωt + 2φ)

21 ry large number of slits in a evice calle a iffraction grat Interference with Three Slits 37.2 Using Figure 37.7 as a moel, sketch the interferen lits. I I max N 2 Primary maximum Seconary maximum N 3

22 Interference Patterns from Many Slits I I max N 2 Primary maximum Seconary maximum N 3 N 4 N 5 For any value intensity in m right of the ce inicate by t is ue to iffra the iniviual iscusse in C N 10 2l l 0 l 2l sin u

23 Diffraction Grating A iffraction grating is a evice that works in a similar way to Young s two slits, but prouces a brighter set of fringes for the same source, an the bright fringes are narrower. It breaks the light from a source up into very, very many coherent sources. (Young s slit oes the same, but only breaks the light into 2 sources.) It is use mainly for spectroscopy (etermining the spectrum of a type of atom or molecule) an in monochromators (evices that select a particular frequency of light).

24 Interference Pattern from a Diffraction Grating A iffraction grating has so many slits that effectively N. With monochromatic light, the peaks are sharp an well-separate. m l l 0 l 2l Figure Intensity versus sin u For light that is compose of several frequencies, the peaks for each will be separate out. sin u for a iffraction grating. The We c spacing lengths wavelen The fir ship sin angle u angles u The monoch princip bright f shoul ecreas

25 Diffraction Gratings There are two types of iffraction grating. Transmission gratings: Incoming plane wave of light Diffraction grating P P First-orer maximum (m 1) Central or zeroth-orer maximum (m 0) First-orer maximum (m 1) Many slits allow light to pass through.

26 Diffraction Gratings Reflection gratings: Light reflects off of a series of mirrore surfaces. 1 lclose/a302/lecture14/lecture 14.html

27 Diffraction Grating Pattern

28 Diffraction Grating We can fin the maxima (bright fringes) of the pattern prouce in action Patterns an Polarization a iffraction grating in exactly the same way we i for Young s slits. Incoming plane wave of light P First-orer maximum (m 1) Diffraction grating P Central or zeroth-orer maximum (m 0) First-orer maximum (m 1) u u sin u

29 Diffraction Grating Once again, light from ifferent slits interferes constructively when the path iffernce δ = mλ (m is an integer). δ = sin θ Maxima (bright fringes) occur when sin θ max = mλ where m Z

30 such as telescopes, cameras, an eyeglasses. Diffraction 35.4 Analysis Moel: Wave Uner Reflection We alreay know that light an other waves that travel through a small We introuce gap (< λ) the iverge, concept of an reflection that the of waves smaller in a the iscussion gap, the of waves moreon strings in Section As with waves on strings, when a light ray traveling in one ivergence. meium encounters a bounary with another meium, part of the incient light When l,,, the rays continue in a straight-line path an the ray approximation remains vali. When l, the rays sprea out after passing through the opening. When l.., the opening behaves as a point source emitting spherical waves. l,, l l.. a b c The intensity of light in each irection is not the same however. Figure wavelen rier in of iam

31 Diffraction Patterns alternating with ark fringes. Incoming wave Slit min max min u max min max L min Viewing screen a b

32 Diffraction Spikes 1 NASA, ESA, an H. Richer (University of British Columbia); Svon Halenbach

33 Diffraction Spikes in Camera Apertures Iris iaphragms ajust the amount of light allowe into a camera boy. They cause characteristic iffraction patterns on photos taken of bright lights. 1 Wikipeia user Cmglee

34 Diffraction Patterns: Arago Spot Directly in the center of the shaow prouce by a roun object lit with coherent light, a spot of light can be observe! This is calle the Arago spot, Fresnel bright spot, or Poisson spot. 1 Photo taken at Exploratorium in SF, own work.

35 Summary two-slit interference multiple slit interference iffraction gratings Collecte Homework! ue Monay, June 18. Final Exam 9:15-11:15am, Tuesay, June 26. Homework Serway & Jewett: prev: Ch 37, onwar from page OQs: 3, 9; CQs: 3, 5; Probs: 1, 3, 5, 13, 19, 21, 25, 51, 60 new: Ch 38, onwar from page CQs: 5; Probs: 25, 60