1 Chapter 33: Interference and Diffraction Homework: 17, 31, 37, 55 Cover Sections: 1, 2, 3, 4, 6, 7 Omit Sectons: 5, 8 2 Outline: Phase Difference and Coherence Interference in Thin Films Single Slit Diffraction Pattern Two Slit Interference Fraunhofer and Fresnel Diffraction Diffraction and Resolution 3 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. 5 Interference in Thin Films 7 8 Change in Wavelength n = index of refraction 9 10 11 12 Condition: Ray 1 and 2 will be out of phase by radians for 589nm light. Path difference = 2t. Two-Slit Interference Pattern 14 15 central max m = 1 bright fringe y-axis m = 2 bright fringe m = 1 dark fringe m = 2 dark fringe m = 3 dark fringe bright/dark are symmetric L 16 17 18 19 Example: slit-separation d = 1.5mm. Light = 589nm. Bright fringes occur at: etc. 20 Example: L = 3m. slit-separation d = 1.5mm. Light = 589nm. Bright fringe spacing = y3 y2 = 1.17 mm 21 Example: slit-separation d = 1.5mm. Light = 589nm. 2 nd Dark fringe occurs at: The 2 nd Dark fringe should occur between 1 st and 2 nd Bright fringes: Diffraction Pattern of a Single Slit 23 24 a = Slit-Width (a d) 25 26 Example: slit-width a = 0.200mm. Light = 589nm. Dark fringes occur at: etc. Using Phasors to Add Harmonic Waves (Omit) Fraunhofer and Fresnel Diffraction 29 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. Diffraction and Resolution 31 First Diffraction Minimum of a Circular Aperture 32 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 1 st minimums of the diffraction patterns fall on the central maximum of the other. A single ellipsoid is seen instead of two separate objects. 33 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: 34 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 Diffraction Gratings Omit End of 33 36 37 38 39