Optics Interference from Films Newton s Rings Michelson Interferometer

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1 Optics Interference from Films Newton s Rings Michelson Interferometer Lana Sheridan De Anza College June 19, 2018

2 Last time diffraction patterns diffraction and interference resolution and Raleigh s criterion reflection and phase changes

3 Overview interference from thin films Newton s rings the interferometer polarization birefringence

4 from a thin film is due to a combination of rays 1 and 2 two surfaces of t reflected from the upper and Reflected ray Consider a film of liquid lower (or surfaces solid) of with the film. refractive indexundergoes n. a pha 2, which is refle 180 phase because it is ref change No phase Therefore, ray 1 change 1 2 ence of l n /2. We before the waves Air sidering light ray n 1.00 A normal, the path Film n t in phase and th constructive interf Thin Film Interference B Air n This condition t Imagine the incident ray shines directly down into the surface. Rays 3 and 4 lead to the two rays (th interference effects for light We draw it making a small angle to the vertical so thatterm we can 1 2l n ). Becau transmitted through the film. clearly see the reflections.

5 Thin Film Interference A B reflected from the upper and lower surfaces of the film. Air n 1.00 Film n Air n phase change No phase change t Reflected undergoes a 2, which is re because it is Therefore, ra ence of l n /2. before the wa sidering light normal, the p in phase and constructive in This conditio the two rays term 1 2l n ). Be Ray 1 undergoes a 180 (ie. λ/2) phase shift at boundary A. Rays 3 and 4 lead to Ray 2 travels an extrainterference distance of 2t effects and has for light a phase shift of 0 at boundary B. transmitted through the film.

6 Thin Film Interference The condition for constructive interference between rays 1 and 2 is: ( 2t = m + 1 ) λ n m Z 2 where λ n = λ n is the wavelength of the light in the film. We can rewrite this as: ( 2nt = m + 1 ) λ m Z 2 For destructive interference: 2nt = mλ m Z These expressions depend on the choice of media: if there is something other than air below or above the film the conditions will change.

7 Thin Film Interference 1 From Dr. Chris L. Davis s page,

8 Thin Film Interference Oil floating on water on pavement after rain.

9 Iridescence in Biology

10 Iridescence in Biology 1 Left photo by Didier Descouens; right Radislav A. Potyrailo et al. Nature Communications 6: 7959, 2015.

11 Antireflective Coatings Antirelective coatings are used on eyeglasses and camera lenses to cut down on glare and increase the transmitted light. 1

12 Interference by reflection question Quick Quiz One microscope slide is placed on top of another with their left edges in contact and a human hair under the right edge of the upper slide. As a result, a wedge of air exists between the slides. An interference pattern results when monochromatic light is incident on the wedge. What is at the left edges of the slides? (A) a dark fringe (B) a bright fringe (C) impossible to determine 1 Serway & Jewett, page 1144.

13 Interference by reflection question Quick Quiz One microscope slide is placed on top of another with their left edges in contact and a human hair under the right edge of the upper slide. As a result, a wedge of air exists between the slides. An interference pattern results when monochromatic light is incident on the wedge. What is at the left edges of the slides? (A) a dark fringe (B) a bright fringe (C) impossible to determine 1 Serway & Jewett, page 1144.

14 Newton s Rings Newton s rings are another independence pattern, formed when a plano-convex lens rests on a flat surface that can reflect light. They are named for Isaac Newton who studied them after their discovery by Robert Hooke. They were used to assess the quality of lenses.

15 Newton s Rings Light shines from above into the lens and is reflected both from the bottom of the lens and the flat glass plate below. These two rays interfere. R 2 1 r P O a b 1 Figure from Serway & Jewett.

16 Newton s Rings Interference pattern produced with monochromatic light. 1 Photo from Amrita University Vlab.

17 Newton s Rings Interference patterns produced with broad-spectrum light (left), mercury fluorescent (limited spectrum), and monochromatic laser light. 1 Photo by Bob Fosbury.

18 Newton s Rings Computer model of Newton s rings for full visible spectrum illumination. 1 From the Scientific Legal Tourist blog.

19 Newton s Rings The dark rings for a particular wavelength can be found using the same ideas as for the thin film. R 2 1 r P O dark: 2nt a = mλ (lens in air so n = 1) here, t is the depth of the air gap. Newton s Rings t = R R 2 r 2 Another method for observing interference in light waves is to Assuming r R, welens canon use top aof Taylor a flat glass expansion surface as about shown r in = Figure 0 to 37.11a. W the air film between the glass surfaces varies in thickness fro show: contact to some nonzero value at point P. If the radius of cur much greater t than r 2 the distance r and the system is viewed fro light and dark rings 2R is observed as shown in Figure 37.11b. T b

20 Newton s Rings R 2 1 r P O a 2nt = mλ ; t r 2 2R Newton s Rings Using the expression for t and rearranging, we see that dark rings occur at radii: mλr r = n Another method for observing interference in light waves is to lens on top of a flat glass surface as shown in Figure 37.11a. W the air film between the glass surfaces varies in thickness fro contact to some nonzero value at point P. If the radius of cur much greater than the distance r and the system is viewed fro where n = 1 if the lens light isand surrounded dark rings by is observed air. as shown in Figure 37.11b. T discovered by Newton, are called Newton s rings. b

21 Michelson Interferometer The Michelson interferometer is an ingenious device for studying interference, measuring wavelength, measuring path differences, finding optical thicknesses of various optical components, studying quantum effects, and spectroscopy (determining a spectrum from a e Optics source). A single ray of light is split into two rays by mirror M 0, which is called a beam splitter. Light source The path difference between the two rays is varied with the adjustable mirror M 1. Telescope L 2 M 0 L 1 M 1 As M 1 is moved, an interference pattern changes in the field of view. M 2

22 7 Michelson Wave Optics Interferometer A single ray of light is split into two rays by mirror M 0, which is called a beam splitter. Light source The path difference between the two rays is varied with the adjustable mirror M 1. Telescope L 2 M 0 L 1 M 1 As M 1 is moved, an interference pattern changes in the field of view. M 2 Invented by Albert Michelson in 1881, this device featured in two target pattern (corresponding to destructive interference) and M 1 is then moved a particularly distance l/4 toward important M 0, the experiments path difference (and changes lotsby more!): l/2. What was a dark circle at the center now becomes a bright circle. As M 1 is moved an additional distance l/4 thetoward Michelson-Morley M 0, the bright circle experiment becomes a dark (1887) circle again. demonstrated Therefore, the fringe there pattern ishifts no by ether one-half fringe each time M 1 is moved a distance l/4. The wavelength of light is then measured by counting the number of fringe shifts for a given displacement of M 1. If the wavelength is accurately known, mirror displacements can be measured to within a fraction of the wavelength. the LIGO experiment (2015) first experimental detection of gravitational waves

23 7 Wave Optics Michelson Interferometer A single ray of light is split into two rays by mirror M 0, which is called a beam splitter. Light source The path difference between the two rays is varied with the adjustable mirror M 1. Telescope L 2 M 0 L 1 M 1 As M 1 is moved, an interference pattern changes in the field of view. M 2 M 0 is a half-silvered mirror called a beamplitter. It transmits half the light that strikes it and reflects the rest. M 1 is a movable mirror. Using a screw mechanism you can target pattern (corresponding to destructive interference) and M 1 is then moved a distance l/4 toward M 0, the path difference changes by l/2. What was a dark circle at the center now becomes a bright circle. As M 1 is moved an additional distance l/4 verytoward slowly M 0, move the bright it closer circle becomes to or further a dark circle from again. M 0 Therefore,. the fringe pattern shifts by one-half fringe each time M 1 is moved a distance l/4. The wavelength M 2 is of light a fixed is then mirror. measured by counting the number of fringe shifts for a given displacement The telescope of M 1 is. If used the wavelength to view is the accurately interference known, mirror pattern displacements can be measured to within a fraction of the wavelength. that forms. We will see an important historical use of the Michelson interferometer in our

24 Michelson Interferometer The interference effects occur because the two paths for the light can be made different lengths. Let the source be S and the telescope be T. Path 1: S M 0 M 1 M 0 T Path 2: S M 0 M 2 M 0 T The only part that differs is the arm traveled to the mirror M 1 or M 2, so the path difference is δ = 2L 1 2L 2

25 Michelson Interferometer The only part of that differs is the arm traveled to the mirror M 1 or M 2, so the path difference is δ = 2L 1 2L 2 The condition for the δ = 0 fringe to be bright or dark depends on the details of the experimental arrangement (eg. beamsplitter designs and coatings).

point source e 3: The circular fringe interference pattern

26 Michelson Interferometer Interference Patterns white light, tilted mirrors, cube beamsplitter, δ = 0 monochromatic light, point source e 3: The circular fringe interference pattern produced b 1 Left photo by Alain Le Rille; right Univ. of Toronto Physics Dept

27 Gravitational Waves General relativity predicts gravitational waves, similar to electromagnetic waves. However, they are much harder to detect than EM waves! Massive objects that accelerate (for example, rotation of a non-rotational symmetric object) generate gravitational waves. Their effect is to distort spacetime as they propagate. They can tell us about events in the cosmos that we cannot see, and they can travel through matter with almost no scattering.

28 Laser Interferometer Gravitational-Wave Observatory (LIGO) Two miles-long interferometers where constructed in Hanford, Washington, and in Livingston, Louisiana. 1 The LIGO Livingston Observatory in Louisiana. Caltech/MIT/LIGO Lab

29 Detecting Gravitational Waves

30 Laser Interferometer Gravitational-Wave Observatory (LIGO) On Sept 14, 2015, both interferometers observed the same pattern of lengthening and contraction in the arms of their interferometers at basically the same time. They concluded that the source of the waves was the merger of two black holes. This was the first confirmed detection of gravitational waves.

31 Laser Interferometer Gravitational-Wave Observatory (LIGO) On Sept 14, 2015, both interferometers observed the same pattern of lengthening and contraction in the arms of their interferometers at basically the same time. They concluded that the source of the waves was the merger of two black holes. This was the first confirmed detection of gravitational waves. Four black hole collisions have now been observed by LIGO, and one of those also by Virgo, a new interferometer in Italy. They have also detected a collision of neutron stars (Aug 17, 2017), the first time both gravitational and EM waves were seen from the same event. The Fermi gamma ray space telescope detected a coinciding short gamma ray burst.

32 Summary interference from thin films Newton s rings the interferometer Final Exam 9:15-11:15am, Tuesday, June 26. Homework Serway & Jewett: prev: Ch 37, onward from page OQs: 5, 7; Probs: 35, 61, 67, (31, 37, 40 covered today) new: Ch 37, onward from page OQs: 1, 5, 7; Probs: 43, 54, 63, 65, 68

Optics Polarization. Lana Sheridan. June 20, De Anza College

Optics Polarization. Lana Sheridan. June 20, De Anza College Optics Polarization Lana Sheridan De Anza College June 20, 2018 Last time interference from thin films Newton s rings Overview the interferometer and gravitational waves polarization birefringence 7 Michelson