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Lecture 16 Interference

Lecture 16 Interference. Chapter 24.1  24.4. Outline. Conditions for Interference Experiments Showing Interference Interference in Thin Films. Wave Optics. Geometric optics considers light as rays. Wave optics applies to wave properties of light.

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Lecture 16 Interference

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  1. Lecture 16Interference Chapter 24.1  24.4 Outline • Conditions for Interference • Experiments Showing Interference • Interference in Thin Films

  2. Wave Optics Geometric optics considers light as rays. Wave optics applies to wave properties of light. Interference is a superposition of two or more waves. It can be constructive or destructive. Interference Demonstration • Conditions for interference: • The waves must maintain a constant phase shift between them (coherency) • The wave must have identical wavelengths

  3. Young’s Double Slit Experiment Demonstration Double slit interference Assumption: The two waves travel in parallel lines (the wave source at infinity). Constructive interference: the path difference is an integer multiple of the wavelength : d sin  = m . Destructive interference, the path difference is an odd multiple of /2 : d sin  = (m+1/2) . d  distance between the slits, m  the order number,   angle between the slit line and the wave direction,   wavelength.

  4. Wavelength Measurement The double slit experiment allows to measure . Assumption: is small, so sin   tan  L is the distance between the slits and the screen, y is the distance between the normal to the screen and the image position. L y =  m d y = L tan   L sin  For bright fringes d sin  = m 

  5. Problem with Double Slit Problem: The double slit is at 0.80 m from the screen. If the distance between alternating bright fringes is 0.95 cm and  = 580 nm, what is the slit separation (d)? 1 nm = 109 m L = 80 cm dy = 0.95 cm L yb =  m d L dy =  d L d =  dy  d = 4.9 105 m = 49 microns (m)

  6. Interference from Reflection Interference can be produced by reflection: Lloyd’s mirror. One wave goes directly to the viewing point, while the other one is reflected off a mirror. Reflection produces a 180o phase shift. Result: the positions of the bright and dark fringes are reversed compared to the double slit interference.

  7. Interference in Thin Films Thin films have two surfaces, producing reflection and causing interference. Consider a film of uniform thickness d and index of refraction n. Definitions: if a EM wave travels from a medium with index of refraction n1 to that of n2 and n2 > n1, it undergoes a 180o phase change. No phase change in the reflected wave if n2 < n1. Also, n = /n. Constructive interference: 2nd = (m+1/2) , m=0,1,2…

  8. Newton Rings Newton rings are circular interference fringes observed through a planoconvex lens. The film in this case is air n = 1. Radii of the dark fringes (rings): rd (mR) Radii of the bright rings: rb(2m+1)R/2 R is the radius of curvature, m is any integer number including 0,  is wavelength.

  9. Interference is one of the wave-like properties of EM waves. Interference can be constructive or destructive. Reflection in a material with a higher index of refraction inserts a 180o phase change in the reflected wave. Summary

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