1. WEEK # 4 Physics-II (Ph-1002) Reflective and non-reflective coatings
Michelson interferometer
Michelson Morley Experiment
Diffraction: Fresnel and Fraunhofer diffraction,
diffraction and Huygen’s principle,
Diffraction from single slit
Book:
“University Physics” by Young & Freedman 13th Edition

2. Anti-Reflective Coating
An 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.

3. Anti-Reflective Coating

4. Anti-Reflective Coating
(Condition)=> nthin layer of hard transparent material < nglass
Same phase change occurs in both reflections .
If the film thickness = λ/4
so total path difference = λ/2 (destructive interference)
Film thickness is often taken at λ =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.

5. Condition => nthin layer of hard transparent material > nglass
Reflective Coating
Condition => nthin layer of hard transparent material > nglass
180o (λ/2 ) phase change occurs at the air–film interface but none at film–glass interface
If film thickness = λ/4
The total path difference=λ/4+λ/4 = λ/2 (constructive interference)

6. Reflective Coating
Example: 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.

7. CD’s and DVD’s Data is stored digitally
A series of ones and zeros read by laser light reflected from the disk
Strong reflections correspond to constructive interference
These reflections represent zeros (0’s)
Weak reflections correspond to destructive interference
These reflections are chosen to represent ones (1’s)

8. CD’s A CD has multiple tracks
The tracks consist of a sequence of pits of varying length formed in a reflecting information layer
The pits appear as bumps to the laser beam
The laser beam shines on the metallic layer through a clear plastic coating

9. Reading a CD
As 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

10. Reading a CD
When 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 area
This ensures destructive interference and very low intensity when the reflected beams combine at the detector
The bump edges are read as ones
The flat bump tops and intervening flat plains are read as zeros

11. DVD’s DVD’s use shorter wavelength lasers
The track separation, pit depth and minimum pit length are all smaller
Therefore, the DVD can store about 30 times more information than a CD

14. 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 DVD

15. Michelson interferometer
The 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.

16. Experimental Setup

17. Working
Light from a monochromatic source S is divided by a beam splitter (BS),
Beam Splitter is oriented at an angle 45° to the beam, producing two beams of equal intensity.
The transmitted beam (T) travels to mirror M1 and it is reflected back to BS. 50% of the returning beam is then reflected by the 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.

18. Compensator
Since 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 M2 passes through the beam splitter three times, while the ray reflected at M1 travels 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 M1 and BS.

19. Calculations
When the light that comes from M1 undergoes reflection at BS, a phase change of π occurs, which corresponds to a path difference of λ/2. 

20. 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.
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. 

21. Michelson Morley Experiment
Performed by Albert Michelson  ( ) and Edward Morley  ( ) 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.

22. Results
The 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.

23. Diffraction
Huygen’s principle: states that we can consider every point of a wave front as a source of secondary wavelets.
Huygen’s principle requires that the waves spread out after they pass through slits
This spreading out of light from its initial line of travel is called diffraction
In general, diffraction occurs when waves pass through small openings, around obstacles or by sharp edges

24. A single slit placed between a distant light source and a screen produces a diffraction pattern
It will have a broad, intense central band
The central band will be flanked by a series of narrower, less intense secondary bands
Called secondary maxima
The central band will also be flanked by a series of dark bands Called minima

25. The results of the single slit cannot be explained by geometric optics
Geometric optics would say that light rays traveling in straight lines should cast a sharp image of the slit on the screen

26. Types of diffraction: (1) Fresnel diffraction (2) Fraunhofer diffraction
Fresnel 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, 1788–1827).
Fraunhofer Diffraction: (German physicist Joseph von Fraunhofer,1787–1826): 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 (θ = 0) with alternating bright and dark fringes on each side
We will restrict the following discussion to Fraunhofer diffraction, which is usually simpler to analyze in detail than Fresnel diffraction.

27. Single Slit Diffraction
According to Huygen’s principle, each portion of the slit acts as a source of waves
The light from one portion of the slit can interfere with light from another portion
The resultant intensity on the screen depends on the direction θ

29. Destructive interference
will occurs for a single slit as (a/2)sinθdark = mλ/2 from eq. (i) so
sinθdark = mλ/ a (ii)
where m = 1, 2, 3, …
Sign of  indicates that there are symmetric dark
fringes above and below on screen central point as shown in the next figure

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

31. How to find the position of the 1st dark fringes in single slit diffraction?
In previous figure, θ is very small & y1<< L, so we can write
sinθ ≈ tanθ = y1/L (as tanθ= y1/L from previous figure)
y1/L ≈ mλ/a (from eq. (ii)
y1 ≈ mLλ/a ≈ Lλ/ as m= 1 so we can generalized this relation as
ym ≈ mLλ/ a ………………… (iii)
where m = 1, 2, 3, …..

32. Problem: Light of wavelength 5
Problem: Light of wavelength 5.80×102 nm is incident on a slit of width nm. The screen is placed 2.00 m from the slit. Find the position of the first dark fringes and the width of the central bright fringe. Solution: λ=5.80×102 nm = 5.80×102 × 10-9 m
a= mm =0.300× 10-3 m
L= 2m
m = +1 (for upper half in previous figure)
ym ≈ mLλ/ a eq. (iii) from previous slide
y+1 & y-1? & w (width) =?
Put the values in eq. (iii) and simplify as y+1= +3.86× 10-3 m
Put m = -1 in eq. (iii) for lower half & simplify, y-1 = -3.86× 10-3 m
We can get w = difference/addition of y+1 & y-1 (+ve & -ve shows only upper & lower side only).
So, w = 7.72× 10-3 m
See University Physics 13th ed. P for detail

33. That’s all for today !