Physics 2B Wave Optics Interference If two waves exist at the same point in space at the same time, they will interfere with each other. Interference Superposition Principle for Waves The Principle of Linear Superposition : When two or more waves are present simultaneously at the same place, the resultant disturbance is the sum of the disturbances from the individual waves. Overlapping waves do not alter the travel of the other wave. The individual waves move independently of one another. 1
Interference Interference of Sound Waves Constructive Interference Destructive Interference For sound waves, constructive interference occurs when the condensations of the rarefactions from two sounds waves overlap. If the condensation from one sound wave overlaps the rarefaction from another sound wave, destructive interference occurs. Interference of Light Waves Interference of Light Waves Constructive interference occurs when the difference in path length is an integer number of wavelengths. Destructive interference occurs when the difference in path length is an odd integer number of half wavelengths. 2
Index of Refraction Water Waves Spread Out behind a Small Opening speed of light in a vacuum c n speed of light in the material v Slide 17-10 Slide 17-9 Light Waves Also Spread Out Behind a Very Narrow Slit the extent to which a wave bends around the edges of an opening is determined by the ratio of /a Slide 17-11 3
Young s Double Slit Experiment Young s Double-Slit Interference Experiment Slide 17-12 Analyzing the Double-Slit Experiment Young s Double Slit Experiment r dsin m m 0,1,2,3,... m m Bright fringes of a double slit: Dark fringes of a double slit: sin m m 0,1, 2,3,... d 1 sin ( m ) m 0,1,2,3,... 2 d Slide 17-13 4
Bright and Dark Fringes in the Double-Slit Experiment Bright Fringes for a Grating Slide 17-14 Slide 17-17 The Fringes Become Very Narrow as the Number of Slits is Increased A Grating Splits Light into the Wavelengths That Make It Up Slide 17-19 Slide 17-20 5
Gratings grating are incredibly useful (especially in astronomy) because the can be used to accurately measure the wavelength of light. Gratings Accurately measuring the wavelength of light is important because every element (H, He, C, ) can only emit light of very specific wavelengths. Hydrogen From d sin( ) = m you can get the wavelength of light by measuring the angular separation ( ) of the lines: d sin( ) / m Helium Carbon Thin-Film Interference Thin-Film Interference Slide 17-21 6
Phase Changes Due to Reflection Reflections at a Boundary When a wave hits a hard boundary like a wall that is too rigid to shake, the wave will reflect back. Slide 17-22 The reflected wave undergoes a phase change that is equivalent to ½ a wavelength. Reflections at a Boundary Reflections at a Boundary Hard Reflection Soft Reflection A wave reflected from a hard boundary undergoes a phase change equivalent to ½ a wavelength. 7
Reflections at a Boundary Analyzing Thin-Film Interference Hard Reflection Soft Reflection Slide 17-23 8
Huygen s Principle Huygen s principle: Every point on a wave front acts as a point source of tiny wavelets that move forward with the same speed as the wave; the wave front at a later instant is the surface that is tangent to the wavelets. Huygen s Principle Single-Slit Light passing through a narrow slit spreads out beyond the slit. no diffraction with diffraction Light waves from different points within a single slit travel different distances in reaching a screen. Because of this, waves from different points within the slit undergo interference and produce a diffraction pattern of bright and dark fringes. Slide 17-27 9
Even though Young s double-slit experiment in 1801 provided convincing evidence for the wave nature of light, it was very slow in being adopted. In an attempt to disprove the wave nature of light, in 1819 the French Academy of Sciences organized an essay competition on diffraction. Augustin Fresnel won the competition, but most scientists did not believe his theories. Poisson pointed out that if light truly behaved as a wave, then light waves should diffract around the edges of a sphere. If this happened, then there should be a bright spot at the center of the shadow of the sphere. The bright spot would occur because the light diffracting around the edges of the sphere should travel the same distance to the center of the shadow and produce constructive interference. The Fresnel Bright Spot The prize committee organized a test of this prediction and discovered the predicted Fresnel bright spot. 10
from Circular Aperture from Circular Aperture When light passes through a circular aperture such as a lens or the pupil of the eye, it undergoes diffraction and produces a diffraction pattern (interference pattern). Resolving Power 11
from Circular Aperture Because of diffraction, there is a limit to how close two point sources can be and still be resolved as separate. from Circular Aperture Two point sources can barely be resolved as separate if the central maximum from one diffraction pattern overlaps the first minimum from the other. barely resolved from Circular Aperture Pointillism 12
Pointillism Pointillism 13