Physical Optics. Diffraction.

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Logan Horn
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1 Physical Optics. Diffraction. Interference Young s interference experiment Thin films Coherence and incoherence Michelson interferometer Wave-like characteristics of light Huygens-Fresnel principle

2 Interference. Interference = superposition of two (or more) coherent waves that results in a new wave pattern. Coherent = same frequency Examples. (from Phys 213) 1. Standing waves = incident wave + reflected wave 2. Two identical sound sources

3 Young s Double Slit Experiment. Qualitative. To see if the light interferes, we pass it subsequently through two separated slits and see if an interference pattern is produced screen This is an interference pattern! Where crests from S 1 and crests from S 2 meet at the screen, a bright fringe appears. Where crests and troughs meet, a dark fringe appears. 3

4 Young s Double Slit Experiment. Experimental. Example of an interference pattern 4

5 Young s Double Slit Experiment. Quantitative. Basic idea: waves from each slit will, in general, travel different distances to a given point on the screen if they arrive perfectly in phase, they constructively interfere, i.e., they add to one another: bright fringe if they arrive perfectly out of phase, they destructively interfere (as shown below): dark fringe if they arrive in between, they do a little of both: part of fringe pattern in between bright and dark fringes 5

6 Young s Double Slit Experiment. Quantitative. Constructive interference L = dsinθ = mλ, m=0,1,2,.. (bright fringes) Location on the screen Question: what happens to the interference pattern if we use green laser light instead of red? 6

7 Young s double slit experiment. Sample Problem. Monochromatic green light, wavelength 550 nm, illuminates two parallel narrow slits 7.7µm apart. Calculate the angular deviation θ of the third-order (m=3) bright fringe in radians and degrees.

8 Thin Film Interference The colors seen in a soap bubble, or from some oil spilled on the ground, are due to interference effects physics.utoledo.edu www-viz.tamu.edu 8

Thin Film Interference On reflection, waves may experience a phase shift of π or λ/2 Example: pulses on strings a) denser lighter (slower faster): no shift b) lighter

9 Thin Film Interference On reflection, waves may experience a phase shift of π or λ/2 Example: pulses on strings a) denser lighter (slower faster): no shift b) lighter denser (faster slower): λ/2 shift Constructive interference (bright) 2Ln 2 /cosθ = m+½, m=0,1,2, Destructive interference (dark) 2Ln 2 /cosθ = m, m=0,1,2, air soapfilm air 9

10 Thin Film Interference. Sample problem Monochromatic light of λ=624nm is incident perpendicularly on a soap film with n=1.33, suspended in air. What are the least two thicknesses of the film for which the reflections from the film undergo fully constructive interference? 10

11 Thin Film Interference. Sample problem Monochromatic light of λ=400 nm is incident perpendicularly on a soap film with n=1.33, covering glass (n=1.8). What is the least thickness of the film for which the glass is invisible? Can we apply that to stealth technology? 11

12 Thin Wedge Interference A broad beam of light of wavelength 623 nm is sent directly downward through the top plate of a pair of glass plates. The plates are 120 mm long, touch at the left end, and are separated by a wire of diameter mm at the right end. The air between the plates acts as a thin film. How many bright fringes will be seen by an observer looking down through the top plate? 12

14 Coherence and Incoherence You may have noticed that in the Young s double slit experiment, there was a single slit in front But when I used the laser or the microwave apparatus, this single slit was not needed, and yet the interference patterns were essentially the same in all cases

15 Coherence and Incoherence The reason is that Young had to use sunlight sunlight is incoherent light, meaning that the phase difference between the light waves at any two points in space is not constant over time it is nearly constant at small distances, but not constant over distances comparable to d the distance between the double-slits if incoherent light is sent through the double slits, the interference pattern would not be seen the first slit in the Young s experiment insures that the light that hits the double slits hits each slit with the same relative phase We got around this problem by using a coherent emitter of radiation, namely the laser (or the klystron that emitted the microwaves) For incoherent sources intensities add up not field amplitudes! (recall unpolarized light and polarizers)

$Michelson Interferometer 1852-1931 First to measure speed of light (with high precision, 1879) First American Noble Prize winner (1907) Permits measurements of distances as small as a fraction of the$

16 Michelson Interferometer First to measure speed of light (with high precision, 1879) First American Noble Prize winner (1907) Permits measurements of distances as small as a fraction of the wavelength of light used Principle of operation: light from source S goes to partially silvered mirror, M transmits some of light, reflects rest light goes to mirror M 1 or M 2, and back to M, traveling distances 2d 1 and 2d 2, respectively these two light waves interfere and this interference pattern is seen by the observer if one mirror (say M 2 ) is moved by l/4, the observer will see (say) a dark fringe change into a bright fringe Applications: LIGO! LIGO! (recitation)

17 Huygens-Fresnel principle Each point reached by a wave acts as a (point) source of secondary waves New wavefront is the result of interference of the secondary waves Later supplemented by Kirchhoff ( ) (Phys 212 fellow)

18 Huygens-Fresnel principle. Propagation of light Refraction of light 18

19 Recap Thin films-bright Thin wedge - # fringes Double Slit-bright 2L = (m+½)(λ/n) m=[2ln/ l -½] L = dsinθ = mλ Michelson Interferometer Shift one mirror arm, see change in fringes

20 Next Time Diffraction Quantifying single slit diffraction Intensity in single slit diffraction circular aperture diffraction double slit diffraction Diffraction gratings

Chapter 28 Physical Optics: Interference and Diffraction

$Chapter 28 Physical Optics: Interference and Diffraction$ Chapter 28 Physical Optics: Interference and Diffraction 1 Overview of Chapter 28 Superposition and Interference Young s Two-Slit Experiment Interference in Reflected Waves Diffraction Resolution Diffraction