1. Lecture 16 Interference 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. Conditions for interference: The waves must maintain a constant phase shift between them (coherency)phase The wave must have identical wavelengths Interference DemonstrationDemonstration Interference is a superposition of two or more waves. It can be constructive or destructive.superposition

3. Young’s Double Slit Experiment DemonstrationDouble slit interference 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). Assumption: The two waves travel in parallel lines (the wave source at infinity). 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. y = L tan   L sin  d sin  = m L y =  m d For bright fringes

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 y b =  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 180 o phase shift.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.film Definitions: if a EM wave travels from a medium with index of refraction n 1 to that of n 2 and n 2 > n 1, it undergoes a 180 o phase change. No phase change in the reflected wave if n 2 < n 1. 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.planoconvex The film in this case is air  n = 1.air Radii of the dark fringes (rings): r d   (m R) Radii of the bright rings: r b  (2m+1)R /2  R is the radius of curvature, m is any integer number including 0, is wavelength.

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