Ch 24 Wave Optics concept questions #8, 11 problems #1, 3, 9, 15, 19, 31, 45, 48, 53
Light is a wave so interference can occur. Interference effects for light are not easy to observe because of the short wavelength. Two conditions to observe sustained interference: 1) the sources must be coherent, they emit waves with a constant phase with respect to each other. 2) The waves have identical wavelengths
Incoherent when the phase between two waves is not constant. Ordinary light bulbs make incoherent light. The conditions for constructive/destructive interference only last for about 10-8 s for incoherent light. Too fast to visually observe.
Easy way to produce coherent light sources. Pass monochromatic light (light with 1 wavelength) through a slit. The first slit creates a single wave front that lights up two more slits, equally spaced from the first. The second pair of slits then act as a pair of coherent light sources.
Young s Double Slit experiment Observes interference pattern from light emerging from two slits (pinholes) Observe alternating bright and dark parallel bands (fringes). bright bands show constructive interference dark bands show destructive interference Constructive interference occurs where the light hits the screen in phase. Destructive interference occurs where the light hits the screen out of phase.
Path difference ( ) Path difference is the difference in distances the two waves have to travel. See pictures 24.3 and 24.4 = r 2 r 1 = d sin When is an integer multiple of the wavelength, constructive interference occurs. = d sin bright = m m 0, 1, 2, 3,... bright corresponds to the angle to the bright fringe Central bright fringe corresponds to m = 0. This is called the zeroth-order maximum.
When is an odd multiple of /2, destructive interference occurs and a dark fringe is present. = d sin dark = (m+ ½) m 0, 1, 2, 3,... If m = 0, then = /2 and this corresponds to the first dark spots next to the bright central fringe. To simplify we make assumption that L >> d. The length to the screen is much larger than the slit separation. Also assume that d>>.
Using the previous assumptions, means that the angles bright and dark are small. For small angles: sin So our equations become: d (y/l) = m or y bright = ( L/d)m for bright fringes m 0, 1, 2, 3,... and y dark L d (m 1 2 ) m 0, 1, 2, 3,... for dark fringes
Change of phase due to reflection When light reflects off of a medium that has a higher index of refraction than the initial medium, the electromagnetic wave undergoes a phase change of 180 0. See fig. 24.6 and 24.7 In figure 24.7 the two reflected beam interfere with each other.
Due to the change of phase because of reflection, thin films can produce an interference pattern. Use rule that the wavelength in a medium of index of refraction, n, is: n = /n. Let ray 1 be reflected from the top surface of the film. Its phase changes by 180 0. This is equivalent to a path difference of /2. Ray 2 pass through the film and reflects off the bottom surface before coming back out the top. If the thickness of the film is t, the extra distance traveled by ray 2 is 2t.
Because ray 1 be reflected from the top surface of the film, its phase changes by 180 0. This is equivalent to a path difference of /2. If the extra distance traveled by ray 2 is an odd multiple of n/2 the two waves recombine in phase and constructive interference occurs. 2t = (m + ½) n m = 0, 1, 2, 3, subtituting n = /n we get: 2nt = (m + ½ ) m = 0, 1, 2, 3,
Destructive interference in a thin film happens when the extra distance traveled by ray 2 is a multiple of n. For destructive interference in a thin film: 2nt = m m = 0, 1, 2, 3, See page 794 for thin film interference strategies. Not the dependence on the number of phase reversals. See examples 24.2 and 24.3
Diffraction When a wave front passes through a small space or around a sharp edge, the shape of the wave front changes. For example when plane waves pass through a thin slit, spherical waves come out. See fig. 24.13 Fig. 24.14 shows the pattern formed by a single narrow slit.
Single slit diffraction When light passes through a slit, light from the different portions of the slit will interfere with light from other portions of the slit. All the light at the slit is in phase. Notice that some rays of the light have to travel farther than others. See 24.17 Destructive interference occurs on the screen at angles, where: sin dark = m /a m 1, 2, 3,... a = slit width
Diffraction grating Tool to analyze light sources. Consists of a large number of equally spaced parallel slits. Made by scratching parallel lines on a glass plate. Typical grating has several thousand lines per centimeter.
Polarization Light is a wave. (Electromagnetic wave) Polarization is good evidence that electromagnetic waves are transverse. E-m waves consist of oscillating electric and magnetic field oriented at 90 degree angles. See fig. 24.24 Conventionally, the polarization corresponds to the orientation of the electric field.
When charges vibrate, they act like tiny antennas. The electric field will oscillate in the direction of the vibration. Because vibration can occur in all directions, the resultant e-m wave is a superposition of the waves produced by the vibrating charges. This results in unpolarized light. If the electric field vibrates in the same direction every time, linearly polarized light is produced. See figure 24.25
Polarizer = material that polarizes light through the selective absorption by aligned molecules. The molecules absorb light that has an electric field parallel to their length. They transmit light that has an electric field perpendicular to their length. The direction perpendicular to the length of the molecules is called the transmission axis. Any light with an electric field perpendicular to the transmission axis is absorbed. See figure 24.26
Polarizing light reduces the intensity of the light that passes through the polarizer. When unpolarized light passes through a polarizer, half the intensity is transmitted. When light reaches a second polarizer, (called an analyzer), the transmitted beam s intensity depends on the angle between polarizers. I = I 0 cos 2 Figure 24.27 All the light is blocked when the two polarizers have their transmission axis at 90 0 angles. http://www.loncapa.org/~mmp/kap24/polarizers/polarizer.htm
Polarization by reflection When unpolarized lights is reflected from a surface, the reflected beam is either completely polarized, partially polarized, or unpolarized depending on the angle of incidence. For one special angle of incidence, the reflected light is completely polarized. See figure 24.28
Brewster s angle is the angle of incidence that results in the reflected beam being totally polarized. n = tan p n is the index of refraction of the reflecting medium. p = tan -1 n For glass n = 1.52 p = 56.7 0 For water n = 1.33 p= 53.1 0