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Book: University Physics by Young & Freedman 13th Edition

Reflective and non-reflective coatingsMichelson interferometerMichelson Morley ExperimentDiffraction: Fresnel and Fraunhofer diffraction, diffraction and Huygens principle, Diffraction from single slit

Physics-II (Ph-1002)WEEK # 4

1Anti-Reflective CoatingAn antireflective or anti-reflection (AR) coating is a type of optical coating applied to the surface of lenses and other optical elements to reduce reflection. In typical imaging systems, this improves the efficiency since less light is lost. In complex systems such as a telescope, the reduction in reflections also improves the contrast of the image by elimination of stray light.2

Anti-Reflective Coating3

Anti-Reflective Coating(Condition)=> nthin layer of hard transparent material < nglass

Same phase change occurs in both reflections .If the film thickness = /4 so total path difference = /2 (destructive interference)Film thickness is often taken at =550 nm (because at this human eye more sensitive)Reflection reduces from ~5% to 1%, light that is not reflected will be transmitted. Application: The same principle is used to minimize reflection from silicon photovoltaic solar cells (n=3.5) by use of a thin surface layer of silicon monoxide (SiO2, n=1.5) this helps to increase the amount of light that actually reaches the solar cells.

4Reflective CoatingCondition => nthin layer of hard transparent material > nglass

180o (/2 ) phase change occurs at the airfilm interface but none at filmglass interfaceIf film thickness = /4 The total path difference=/4+/4 = /2 (constructive interference)

5Reflective CoatingExample: a coating with n=2.5 causes 38% of the incident energy to be reflected, compared with 4% or so with no coating. By use of multiple-layer coatings, it is possible to achieve nearly 100% transmission or reflection for particular wavelengths.Some practical applications of these coatings are for color separation in television cameras and for infrared heat reflectors in motion picture projectors, solar cells, and astronauts shades.

6CDs and DVDsData is stored digitallyA series of ones and zeros read by laser light reflected from the diskStrong reflections correspond to constructive interferenceThese reflections represent zeros (0s)Weak reflections correspond to destructive interferenceThese reflections are chosen to represent ones (1s)

7CD (Compact Disk)A CD has multiple tracks The tracks consist of a sequence of pits of varying length formed in a reflecting information layerThe pits appear as bumps to the laser beamThe laser beam shines on the metallic layer through a clear plastic coating

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Reading a CD9As the disk rotates, the laser reflects off the sequence of bumps and lower areas into a photodector

The photodector converts the fluctuating reflected light intensity into an electrical string of zeros & ones

The pit depth is made equal to one-quarter of the wavelength of the light

Reading a CD10When the laser beam hits a rising or falling bump edge, part of the beam reflects from the top of the bump and part from the lower adjacent areaThis ensures destructive interference and very low intensity when the reflected beams combine at the detectorThe bump edges are read as onesThe flat bump tops and intervening flat plains are read as zeros

DVD (Digital Video Disc)DVDs use shorter wavelength lasersThe track separation, pit depth and minimum pit length are all smaller

Therefore, the DVD can store about 30 times more information than a CD1112

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The Blu-ray Disc is an optical disc with the same dimensions as the DVD disc: 12 cm in diameter and 1.2 mm in thickness. By using a combination of 405 nm wavelength blue-violet laser, which is shorter wavelength than red laser used by DVD14

Michelson interferometer

15The Michelson interferometer is the best example of what is called an amplitude-splitting interferometer.

It was invented in 1893 by Albert Michelson.

The Michelson interferometer produces interference fringes by splitting a beam of monochromatic light so that one beam strikes a fixed mirror and the other a movable mirror. When the reflected beams are brought back together, an interference pattern results.

With an optical interferometer, one can measure distances directly in terms of wavelength of light used, by counting the interference fringes that move when one or the other of two mirrors are moved.

Experimental Setup16

WorkingLight from a monochromatic source S is divided by a beam splitter (BS),Beam Splitter is oriented at an angle 45to the beam, producing two beams of equal intensity. The transmitted beam (T) travels to mirror M1and it is reflected back to BS. 50% of the returning beam is then reflected bythe beam splitter and strikes the screen, E. The reflected beam (R) travels to mirror M2, where it is reflected. 50% of this beam passes straight through beam splitter and reaches the screen.17

CompensatorSince the reflecting surface of the beam splitter BS is the surface on the lower right, the light ray starting from the source S and undergoing reflection at the mirror M2passes through the beam splitter three times, while the ray reflected at M1travels through BS only once. The optical path length through the glass plate depends on its index of refraction, which causes an optical path difference between the two beams. To compensate for this, a glass plate CP of the same thickness and index of refraction as that of BS is introduced between M1and BS.18Calculations19

When the light that comes from M1undergoes reflection at BS, a phase change ofoccurs, which corresponds to a path difference of /2.

Imaging Cells with a Michelson Interferometer

This false-color image of a human colon cancer cell was made using a microscope that was coupled to a Michelson interferometer. The cell is in one arm of the interferometer, and light passing through the cell undergoes a phase shift that depends on the cell thickness and the organelles within the cell.The fringe pattern can then be used to construct a three-dimensional view of the cell. Scientists have used this technique to observe how different types of cells behave when prodded by microscopic probes.Cancer cells turn out to be softer than normal cells, a distinction that may make cancer stem cells easier to identify.20

Other Applications

1. The Michelson - Morley experiment is the best known application of Michelson Interferometer.2. They are used for the detection of gravitational waves.3. Michelson Interferometers are widely used in astronomical Interferometry.Michelson Morley Experiment 21Performed byAlbert Michelson (1852-1931) andEdward Morley (1838-1923) in 1887.Prevailing theories held that ether formed an absolute reference frame with respect to which the rest of the universe was stationary. It would therefore follow that it should appear to be moving from the perspective of an observer on the sun-orbiting Earth. As a result, light would sometimes travel in the same direction of the ether, and others times in the opposite direction. Thus, the idea was to measure the speed of light in different directions in order to measure speed of the ether relative to Earth, thus establishing its existence.

ResultsThe light would travel faster along an arm if oriented in the "same" direction as the ether was moving, and slower if oriented in the opposite direction. Although Michelson and Morley were expecting measuring different speeds of light in each direction, they found no discernible fringes indicating a different speed in any orientation or at any position of the Earth in its annual orbit around the Sun.22DiffractionHuygens principle: states that we can consider every point of a wave front as a source of secondary wavelets.Huygens principle requires that the waves spread out after they pass through slitsThis spreading out of light from its initial line of travel is called diffractionIn general, diffraction occurs when waves pass through small openings, around obstacles or by sharp edges

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A single slit placed between a distant light source and a screen produces a diffraction patternIt will have a broad, intense central bandThe central band will be flanked by a series of narrower, less intense secondary bandsCalled secondary maximaThe central band will also be flanked by a series of dark bands Called minima24The results of the single slit cannot be explained by geometric opticsGeometric optics would say that light rays traveling in straight lines should cast a sharp image of the slit on the screen

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Types of diffraction: (1) Fresnel diffraction (2) Fraunhofer diffractionFresnel diffraction: both the point source and the screen are relatively close to the obstacle forming the diffraction pattern. This situation is described as near-field diffraction or Fresnel diffraction, pronounced Freh-nell(French scientist Augustin Jean Fresnel, 17881827).Fraunhofer Diffraction: (German physicist Joseph von Fraunhofer,17871826): occurs when the rays leave the diffracting object in parallel directions Screen very far from the slit, converging lens (shown). A bright fringe is seen along the axis ( = 0) with alternating bright and dark fringes on each side

26We will restrict the following discussion to Fraunhofer diffraction, which is usually simpler to analyze in detail than Fresnel diffraction.Single Slit DiffractionAccording to Huygens principle, each portion of the slit acts as a source of wavesThe light from one portion of the slit can interfere with light from another portionThe resultant intensity on the screen depends on the direction

2728Destructive interference

will occurs for a single slit as (a/2)sindark = m/2 from eq. (i) so sindark = m/ a --------------(ii) where m = 1, 2, 3, Sign of indicates that there are symmetric darkfringes above and below on screen central point as shown in the next figure

29The general features of the intensity distribution are shownA broad central bright fringe is flanked by much weaker bright fringes alternating with dark fringesThe points of constructive interference lie approximately halfway between the dark fringes

30How to find the position of the 1st dark fringes in single slit diffraction?

In previous figure, is very small & y1