Wave Optics Light interferes constructively and destructively just as mechanical waves do. However due to the shortness of the wave length (4-7 x m) it is difficult to observe unless the follow is met, 1) the sources must be coherent ( waves must be in constant phases with each other) 2) Waves must have identical wavelengths.

Cont. Ordinary light undergoes random changes every s, thus interference patterns occur at about the same time duration. Eyes are incapable of follow such shortness of time so ordinary light is said to be incoherent. If light is passed through a single small slit a single wave front is produced. If that front then passes through a double slit the two fronts now produced will be coherent and interference can be observed.

Young’s Double Slit Experiment In 1801 Thomas Young demonstrated light interference by passing monochromatic light through a single slit which then passed through a double slit and the resulting interference pattern was displayed on a screen. The pattern produced was a series of bright (constructive) and dark (destructive) bands called fringes.

Cont. Constructive interference occurs because the distance traveled by each wave from the two slits is exactly one or a whole multiple of a wavelength in difference. Destructive interference occurs because the distance traveled by the waves is 1/2 wavelength in difference resulting in crest matching a trough.

Cont. d r1 r2  Slit distance = d r2-r1 =  = d sin  p= first bright band L y o p  Distance to screen 

Cont. Constructive interference occurs at p  = d sin  bright = m where m = 1,2,3,…… m is the order number the central bright fringe is at m = 0 Destructive interference occurs at at odd multiples of /2  = d sin  dark = (m +1/2) when m = 0 it is the location of the first dark fringe.

Cont. Instead of using an angle to find fringes, it is possible to relate the vertical distance y to L where y bright = [( L)/d]m m= 1,2,…… and y dark = [( L)/d](m +1/2) m= 1,2,…… This is valid when L>>d and d>> Young’s slit experiment gave the wave theory of light credibility as it was not conceivable for particles to cancel each other

Change of Phase due to Reflection An electromagnetic wave undergoes a phase change of 180 degrees upon reflection from a medium that has an index of refraction higher than the one in which the wave was traveling. There is no phase change when the wave is reflected from the boundary of a medium with a lower index of refraction.

Lloyd’s Mirror S’ S p P’ mirror screen Real source Light can arrive at p from either source. Because s and s’ differ in phase by 180 o the fringe pattern is reversed to that of Young’s. there will be dark fringe at p. Virtual source

Interference in Thin Films The interference effects seen in soap bubbles and thin oil films results from the interference occurring from the reflection of waves from the two surfaces of the film. air Film with index n phase change No phase change t 1 2

Cont. Waves traveling from medium with n 1 to medium of n 2 where n 2 > n 1 undergo 180 o phase change The wavelength of light n = /n where = wavelength in a vacuum. Ray 1 undergoes a phase change ray 2 does not because n 1 <n 2 Ray 2 travels 2t, if 2t = /2 then rays are in phase

Cont. For constructive interference in thin films 2nt = (m+1/2) m= 1,2,…….. For destructive interference 2nt = m m= 1,2,……. These equations are only valid if there is only one phase reversal.

Diffraction Diffraction occurs when waves pass through small openings, around obstacles or pass sharp edges. After passing such opening straight wave fronts spread out forming spherical wave fronts. When light passes a single slit it produces a pattern on a screen that has one intense central band flanked by a series of less intense secondary bands (secondary maxima), and a series of dark bands minima.

Single Slit Diffraction Fraunhofer diffraction occurs when rays leave a diffracting object in parallel directions. This can be demonstrated with single slit diffraction. Huygen’s principle states that each portion of a slit acts as a source of waves. Hence, light from one portion of the slit can interfere with light from another portion. The resultant intensity on a screen depends on the direction .

Cont. Wave 1 travels farther than wave 2 by a/2sin  as do waves 3 and 5 where a is the width of the slit a/ a/2 sin   a

Cont. If the path difference is exactly half of a wavelength destructive interference occurs. a/2 sin  = /2 or sin  = /a AS dark bands will occur at full intervals of then sin  dark = m ( /a) m= 1,2,… Points of constructive interference lie approximately halfway between the dark fringes. The central bright fringe is twice as wide as maxima having m>1.

Diffraction Grating A device used to analyze light sources, it consists of a large number of slits (gratings), say 5000/cm. This can be accomplished by scratches on a hardened surface. The spacing d, between the lines is equal to the reciprocal of the number 1/5000 or 2x Each slit acts as a wave source causing an interference pattern. If the path difference is a whole multiple of a wavelength waves are in phase producing a maxima.

Cont. A maxima will occur at d sin  bright = m where m = 1,2,……( the order number) Zeroth-order maximum when m = 0,  = 0 The first order maximum, m= 1 sin  = /d. The second order m= 2, sin  = 2 /d, etc. Light emerging at an angle other than that for a maxima will produce destructive interference. A spectroscope, (grating, lens and telescope combination) is used to measure wavelengths.

Polarization of Light Waves Electromagnetic waves are electric and magnetic field vectors perpendicular to each other, that propagate perpendicularly to the direction of travel. Ordinary light consists of a large number of electromagnetic waves, originating from the vibration of atoms, all with varying orientations. The resultant electromagnetic wave is a superposition of waves unpolarized.

Cont. A wave is linearly polarized (polarized) if the electric field at all times is in the same direction. The plane formed by the electric field as the wave propagates is called the plane of polarization. Polarization can be obtained by removing all waves except those oscillating in the same direction, by selective absorption, reflection and scattering

Selective Absorption Polarized material consisting of long hydrocarbon chains that are stretched and aligned during manufacturing, and dipped into iodine to become electrical conductors. Absorption of all wavelengths of light except those with electric field perpendicular to the plane to the alignment, ( transmission axis).

Malus’s Law Consider two polarized sheets the first (incident light) is called the polarizer, the second is called the analyzer. The component E o that is parallel to the analyzer is allowed to pass through. The intensity of the beam that passes through the analyzer is I = I o cos 2  (Malus’s Law) where I o = the intensity of the wave on the analyzer.

Polarization by Reflection Depending on the angle of incidence reflected light can be polarized, unpolarized (0 o or 90 o ), or partially polarized. Brewster’s law, when the incident angle is  p (Brewster’s angle, polarizing angle), then all light is polarized, that is n = tan  p All other angles cause partial polarization.

Polarization by Scattering When light is incident on particles ( gas) the electrons can absorb and reradiate part of the light. This effect by the medium (scattering) causes sunlight from directly overhead to be polarized. Optical Activity. A substance is optically active if it rotates the plane of polarization. Optical activity occurs because of the asymmetry of the constituent molecules.

Assignment (Oh Yeah!) Read about CD’s DVD’s, diffraction on CD’s and liquid crystals. Write a brief outline of each.