Review of Waves. You are expected to recall facts about waves from Physics 1135.

Transcription

1 Toda s agenda: eview of Waves. You are expected to recall facts about waves from Phsics Young s Double Slit Experiment. You must understand how the double slit experiment produces an interference pattern. Conditions for Interference in the Double Slit Experiment. You must be able to calculate the conditions for constructive and destructive interference in the double slit experiment. Intensit in the Double Slit Experiment. You must be able to calculate intensities in the double slit experiment.

2 eview of Waves Wave: variation (disturbance) of phsical quantit that propagates through space often: oscillation in space and time (x,t) A sin (kx ωt). phase of this wave θ(x,t) kx ωt. x if ou are moving with the wave, phase is constant (for =/2, ou sit at the maximum)

3 How fast does the wave move? if is constant with time dθ dx 0 k ω. dt dt phase velocit: dx v p. dt k x Imagine ourself riding on an point on this wave. The point ou are riding moves to the right. The velocit it moves at is v p. If the wave is moving from left to right then /k must be positive.

4 Superposition a Characteristic of All Waves When waves of the same nature arrive at some point at the same time, the corresponding phsical quantities add. Example: If two electromagnetic waves arrive at a point, the electric field is the sum of the (instantaneous) electric fields due to the two waves. Implication: Intensit of the superposed waves is proportional to the square of the amplitude of the resulting sum of waves.

5 Interference a esult of the Superposition of Waves Constructive Interference: If the waves are in phase, the reinforce to produce a wave of greater amplitude. Destructive Interference: If the waves are out of phase, the reinforce to produce a wave of reduced amplitude.

6 Optical path length difference two sources emit waves in phase waves travel different distances L 1 and L 2 to point of interest optical path difference L = L 1 -L 2 determines interference 4 5 L = m In phase constructive L = (m+1/2) Out of phase destructive

7 Toda s agenda: eview of Waves. You are expected to recall facts about waves from Phsics Young s Double Slit Experiment. You must understand how the double slit experiment produces an interference pattern. Conditions for Interference in the Double Slit Experiment. You must be able to calculate the conditions for constructive and destructive interference in the double slit experiment. Intensit in the Double Slit Experiment. You must be able to calculate intensities in the double slit experiment.

8 Young s Double Slit Experiment famous experiment, demonstrates wave nature of light single light source illuminates two slits, each slit acts as secondar source of light light waves from slits interfere to produce alternating maxima and minima in the intensit eference and tos: fsu magnet lab, Colorado light cannon, wave interference, double slit.

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11 How does this work? At some locations on the screen, light waves from the two slits arrive in phase and interfere constructivel. At other locations light waves arrive out of phase and interfere destructivel.

12 Conditions for Interference Wh the double slit? Can't I just use two flashlights? sources must be coherent - maintain a constant phase with respect to each other sources should be monochromatic - contain a single wavelength onl

13 Toda s agenda: eview of Waves. You are expected to recall facts about waves from Phsics Young s Double Slit Experiment. You must understand how the double slit experiment produces an interference pattern. Conditions for Interference in the Double Slit Experiment. You must be able to calculate the conditions for constructive and destructive interference in the double slit experiment. Intensit in the Double Slit Experiment. You must be able to calculate intensities in the double slit experiment.

14 For an infinitel distant* screen: L 1 L 1 S 1 L 2 d S 2 L tan P d L 2 L = L 2 L 1 = d sin *so that all the angles labeled are approximatel equal

15 L 1 Constructive Interference: L d sin m, m=0, 1, 2... d L 2 Destructive Interference: L = L 2 L 1 = d sin 1 L d sin m+, m=0, 1, The parameter m is called the order of the interference fringe. The central bright fringe at = 0 (m = 0) is known as the zeroth-order maximum. The first maximum on either side (m = ±1) is called the first-order maximum.

16 For small angles: tan sin L 1 Bright fringes: d S 1 S 2 L L 2 tan P m m d sin d m d This is not a starting equation! Do not use the small-angle approximation unless it is valid!

17 For small angles: tan sin L 1 Dark fringes: d S 1 S 2 L L 2 tan P 1 m d sin 2 m 1 d 2 1 m d 2 This is not a starting equation! Do not use the small-angle approximation unless it is valid!

18 Example: a viewing screen is separated from the double-slit source b 1.2 m. The distance between the two slits is mm. The second-order bright fringe (m = 2) is 4.5 cm from the center line. Determine the wavelength of the light. tan sin Bright fringes: m m d sin d d m m m m 560 nm 1.2 m 2 7 d S 1 S 2 L L 1 L 2 tan P

19 Example: a viewing screen is separated from the double-slit source b 1.2 m. The distance between the two slits is mm. The second-order bright fringe (m = 2) is 4.5 cm from the center line. Find the distance between adjacent bright fringes. tan sin Bright fringes: m m d sin d d S 1 S 2 L L 1 L 2 tan P m d m1.2 m 2 m+1- m m 1 m m 2.2 cm -5 d d d m

20 Example: a viewing screen is separated from the double-slit source b 1.2 m. The distance between the two slits is mm. The second-order bright fringe (m = 2) is 4.5 cm from the center line. Find the width of the bright fringes. Define the bright fringe width to be the distance between two adjacent destructive minima. dark 1 m d sin d 2 1 dark m d 2 d S 1 S 2 L L 1 L 2 tan P 1 1 dark,m+1-dark,m m 1 m d 2 d 2 d m1.2 m dark,m+1- dark,m 2.2 cm m

21 Toda s agenda: eview of Waves. You are expected to recall facts about waves from Phsics Young s Double Slit Experiment. You must understand how the double slit experiment produces an interference pattern. Conditions for Interference in the Double Slit Experiment. You must be able to calculate the conditions for constructive and destructive interference in the double slit experiment. Intensit in the Double Slit Experiment. You must be able to calculate intensities in the double slit experiment.

22 Intensit in the Double Slit Experiment So far: positions of the minima and maxima of the double-slit interference pattern Now: light intensit at arbitrar location in interference pattern (derivation is in text book)

23 ecall: optical path length difference L = L 1 -L 2 path length difference L= corresponds to phase difference of =2. in general, path length difference L corresponds to phase difference =2L/ for the double-slit L=d sin 2π φ = d sin λ 2π φ = λ L is also "official"

24 Your text writes the equation for the intensit distribution in the in terms of the phase difference on the previous slide. Your starting equation for the intensit is 2 φ I=I 0 cos where I 0 is 4 times the peak intensit of either of the two interfering waves: I 0 =4Isingle wave Wh did m previous diagrams show this?