The dual nature of light: Wave-particle Duality.pptx

Wave particle duality of light

1. WAVE-PARTICLE DUALITY

2. The “shadow” of a horizontal slit as incorrectly predicted by geometric optics. Geometrical optics - describes light propagation in terms of rays - useful in approximating the paths along which light propagates

3. A horizontal slit produces a diffraction pattern For a  

4. Properties of Light: Diffraction Diffraction is the bending of a wave as it passes through a hole or around an obstacle. If light consists of parallel rays, they would travel through a small pinhole and make a small, bright spot on a nearby screen. Effect cannot be explained by ray model of light. Sharp-edged shadow Fuzzy shadow  

5. Diffraction of Waves Observation: A spot larger than the pinhole and varying in brightness. The pinhole somehow affects the light that passes through it. Diffraction is proportional to the ratio of wavelength to width of gap. The longer the wavelength and/or the smaller the gap, the greater the angle through which the wave is diffracted. Fuzzy shadow

6. Diffraction What happens when a planar wavefront of light interacts with an aperture or slit? If the aperture/slit is large compared to the wavelength you would expect this.... …Light propagating in a straight path.

7. If the aperture/slit is small compared to the wavelength would you expect this? Diffraction Not really…

8. In fact, what happens is that: a spherical wave propagates out from the aperture. All waves behave this way. Diffraction This phenomenon of light spreading in a broad pattern, instead of following a straight path, is called: DIFFRACTION If the aperture is small compared to the wavelength, would you expect the same straight propagation? … Not really

9. Huygens’s principle  states, “Every point on a wavefront is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. The new wavefront is a line tangent to all of the wavelets.” Each point on the wavefront emits a semicircular wavelet that moves a distance  s = vt  . The new wavefront is a line tangent to the wavelets.

10. Huygens’s principle applied to a straight wavefront striking an opening. The edges of the wavefront bend after passing through the opening, a process called diffraction. The amount of bending is more extreme for a small opening, consistent with the fact that wave characteristics are most noticeable for interactions with objects about the same size as the wavelength.

11. Diffraction of Waves

12. Properties of Light: Interference and Superposition What happens if two waves run into each other? Waves can interact and combine with each other, resulting in a composite form. Interference is the interaction of the two waves. reinforcing interaction = constructive interference canceling interaction = destructive interference Superposition is the method used to model the composite form of the resulting wave.

13. Interference of Waves Interference: ability of two or more waves to reinforce or cancel each other. Constructive interference occurs when two wave motions reinforce each other, resulting in a wave of greater amplitude. Destructive interference occurs when two waves exactly cancel, so that no net motion remains.

14. I nterference pattern from two-slit diffraction

15. Wave-particle Duality  the Principle of Complementarity Wave model Diffraction Interference Polarization Particle model Photoelectric effect X-ray production Compton scattering

16. Diffraction in the Photon Picture Photomultiplier – detects and counts individual photons at each position Images record the positions where individual photons strike the screen

17. Diffraction in the Photon Picture To reconcile the wave and particle aspect, pattern is treated as a statistical distribution of how many photons go to each spot. Diffraction pattern tells us the probability that any individual photon will land at a given spot. We cannot predict where exactly where an individual photon will go; the diffraction/interference pattern is a statistical distribution.

18. Diffraction in the Photon Picture The wave description, not the particle description, explains the single- and double-slit patterns. The particle description, not the wave description, explains why the photomultiplier records discrete packages of energy. The two descriptions complete our understanding of the results.

19. Probability and Uncertainty We cannot treat a photon as a point object ! Newtonian particle model does not work for photons There are limitations on the precision with which we can simultaneously determine the position and momentum of a photon. Photon’s behavior can only be stated in terms of probabilities.

20. Interpreting single-slit diffraction in terms of photon momentum. If  << a – 85% of photons go into the central maximum of the diffraction pattern  1 – angle between the central maximum and the 1 st minimum For m = 1, with  = a and since sin  1 =  1 ( 1 is very small) Photons may have the same initial state, but they don’t follow the same path. The exact trajectory of photons cannot be predicted. Only describe the probability that a photon will strike a given spot on the screen. Dark fringes: m = 1, 2, 3,…    

21. Interpreting single-slit diffraction in terms of photon momentum. There are fundamental uncertainties in both the position and the momentum of an individual particle, and these uncertainties are related inseparably.     For the 85% of the photons that strike the detector within the central maximum, the p y is spread out in the range to - .  

22. Interpreting single-slit diffraction in terms of photon momentum. However, the symmetry of the diffraction pattern shows us the average value ( p y ) ave = 0. There will be an uncertainty in the y-comp. of momentum at least as great p x /a:    

23. The Uncertainty Principle If a coordinate x has uncertainty x and if the corresponding momentum component p x has an uncertainty  p x , then those standard-deviation uncertainties are found to be related in general by the inequality where:

24. The Uncertainty Principle It states that, in general, it is impossible to simultaneously determine both the position and the momentum of a particle with arbitrarily great precision, as classical physics would predict. Instead, the uncertainties in the two quantities play complementary roles (Complementarity Principle). To detect a particle, the detector must interact with it, and this interaction unavoidably changes the state of motion of the particle, introducing uncertainty about its original state. The uncertainties we have described are fundamental and intrinsic; they cannot be circumvented even in principle by any experimental technique, no matter how sophisticated.

25. Waves and Uncertainty Consider a sinusoidal electromagnetic wave propagating in the positive x-direction with its electric field polarized in the y-direction. If the wave has wavelength frequency and amplitude we can write the wave function as

26. Superposition of two sinusoidal functions: At t = 0: (a) Two sinusoidal waves with slightly different wave numbers and hence slightly different values of momentum shown at one instant of time. (b) The superposition of these waves has a momentum equal to the average of the two individual values of momentum. The amplitude varies, giving the total wave a lumpy character not possessed by either individual wave.

27. Uncertainty in Energy At x = 0: If we replace the x-momentum, p x by energy E and the position x by time t .

28. Ultrashort laser pulses and the uncertainty principle Many varieties of lasers emit light in the form of pulses rather than a steady beam. A tellurium–sapphire laser can produce light at a wavelength of 800 nm in ultrashort pulses that last only 4.00 x 10 -15 s (4.00 femtoseconds, or 4.00 fs). The energy in a single pulse produced by one such laser is 2.00 J = 2.00 x10 -6 J and the pulses propagate in the positive x-direction. Find (a) the frequency of the light; (b) the energy and minimum energy uncertainty of a single photon in the pulse; (c) the minimum frequency uncertainty of the light in the pulse; (d) the spatial length of the pulse, in meters and as a multiple of the wavelength; (e) the momentum and minimum momentum uncertainty of a single photon in the pulse; and (f ) the approximate number of photons in the pulse.