1 Outline: Phase Difference and Coherence Interference in Thin Films Single Slit Diffraction Pattern Two Slit Interference
Fraunhofer and Fresnel Diffraction Diffraction and Resolution 2 3 33-1
Phase Difference and Coherence Phase Difference: The fractional part of a period which represents the offset in peak positions of waves. Coherence: The existence of a correlation between the phases of two or more waves such that interference effects can be observed.
Interference: The variation with distance or time of the amplitude of a wave which results from the superposition of two or more waves. 4 5
33-2 Interference in Thin Films 6 7
Change in Wavelength c f v f n n
n n = index of refraction 8
9 10 11
Condition: Ray 1 and 2 will be out of phase by radians for 589nm light. Path difference = 2t. 2t
2 9 589 10 m / 1.33 5.32t 589 10 9 m t 110 nm 0.110 m
12 33-3 Two-Slit Interference Pattern 13
14 y-axis bright/dark are symmetric m = 2 bright fringe
L m = 1 bright fringe central max m = 1 dark fringe m = 2 dark fringe m = 3 dark fringe
15 16 17
18 Example: slit-separation d = 1.5mm. Light = 589nm. Bright fringes occur at: 1 sin 1 (1)(589 10 9 m) / 1.5 10 3 m 0.0224
2 sin 1 (2)(589 10 9 m) / 1.5 10 3 m 0.0449 3 sin 1 (3)(589 10 9 m) / 1.5 10 3 m 0.0674 etc. 19 Example: L = 3m. slit-separation d = 1.5mm. Light = 589nm.
y2 (2)(589 10 9 m)(3m) / 1.5 10 3 m 2.36mm y3 (3)(589 10 9 m)(3m) / 1.5 10 3 m 3.53mm Bright fringe spacing = y3 y2 = 1.17 mm 20 Example: slit-separation d = 1.5mm. Light = 589nm.
2nd Dark fringe occurs at: 2 sin 1 (2 12 )(589 10 9 m) / 1.5 10 3 m 0.0337 The 2nd Dark fringe should occur between 1st and 2nd Bright fringes: 0.0224 0.0449
2 0.0337 2 21 33-4 Diffraction Pattern of
a Single Slit 22 23 a = Slit-Width
(a d) 24 25 Example: slit-width a = 0.200mm. Light = 589nm.
Dark fringes occur at: 1 sin 1 (1)(589 10 9 m) / 0.200 10 3 m 0.168 2 sin 1 (2)(589 10 9 m) / 0.200 10 3 m 0.337 etc. 26
(Omit) 33-5 Using Phasors to Add Harmonic Waves 27
33-6 Fraunhofer and Fresnel Diffraction 28
Fraunhofer and Fresnel Diffraction Patterns Fresnel Pattern: observed near obstacle causing diffraction. Fraunhofer Pattern: observed far from away from the obstacle. The criterion for determining near and far is
the convergence angle of the light which makes up the pattern. 29 33-7 Diffraction and Resolution
30 First Diffraction Minimum of a Circular Aperture 1.22 D
31 Rayleigh Criterion occurs when two point sources of light are close enough
together that light coming from them passes through a circular aperture so that the 1st minimums of the diffraction patterns fall on the central maximum of the other. A single ellipsoid is seen instead of two separate objects. 32
Rayleigh Criterion Formula is a condition for the angle of convergence of rays emanating from the objects that pass through the aperture. This angle is called alpha, and occurs when: c 1.22
D 33 Summary: Phase Difference and Path Difference Coherence defined
Interference in Thin Films Single Slit and Two Slit Patterns Fraunhofer and Fresnel Diffraction Diffraction limits ultimate resolution 34
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