Chapter 35. Interference

Size: px
Start display at page:

Download "Chapter 35. Interference"

Transcription

1 Chapter 35 Interference The concept of optical interference is critical to understanding many natural phenomena, ranging from color shifting in butterfly wings to intensity patterns formed by small apertures. These phenomena cannot be explained using simple geometrical optics, and are based on the wave nature of light. In this chapter we explore the wave nature of light and examine several key optical interference phenomena. 35-1

2 Light as a Wave Huygen s Principle: All points on a wavefront serve as point sources of spherical secondary wavelets. After time t, the new position of the wavefront will be that of a surface tangent to these secondary wavelets. Fig

3 Fig Law of Refraction 1 1 v1 t = = = v1 v v 1 sin θ1 = (for triangle hce) hc sin θ = (for triangle hcg) hc sinθ1 1 v1 = = sinθ v c c n1 = and n = v1 v sinθ1 cn1 n sinθ = cn = n 1 n Index of Refraction: sinθ = n sinθ Law of Refraction: 1 1 n = 35-3 c v

4 Wavelength and Index of Refraction n v v n n = c = c = n v c n c f = n f = n = = The frequency of light in a medium is the same as it is in vacuum n Fig Since wavelengths in n1 and n are different, the two beams may no longer be in phase L L Ln1 Number of wavelengths in n1: N = 1 = n1 n = 1 L L Ln Number of wavelengths in n: N = = n n = Ln Ln L Assuming n > n1: N N1 = = ( n n1) 35-4 N N1 = 1/ wavelength destructive interference

5 Rainbows and Optical Interference Fig The geometrical explanation of rainbows given in Ch. 34 is incomplete. Interference, constructive for some colors at certain angles, destructive for other colors at the same angles is an important component of rainbows 35-5

6 Diffraction For plane waves entering a single slit, the waves emerging from the slit start spreading out, diffracting. Fig

7 Young s Experiment For waves entering a two slit, the emerging waves interfere and form an interference (diffraction) pattern. Fig

8 Locating Fringes The phase difference between two waves can change if the waves travel paths of different lengths. What appears at each point on the screen is determined by the path length difference L of the rays reaching that point. Path Length Difference: L= dsinθ Fig

9 Locating Fringes Fig ( )( ) if L= dsinθ = integer bright fringe Maxima-bright fringes: dsin θ = m for m= 0,1,, K ( )( ) if L= dsinθ = odd number dark fringe 1 Minima-dark fringes: θ ( ) dsin = m+ for m = 0,1,, K m 1 = bright fringe at: θ = sin d m = 1 dark fringe at: θ = sin d 35-9

10 Coherence Two sources to produce an interference that is stable over time, if their light has a phase relationship that does not change with time: E(t)=E 0 cos(ωt+φ) Coherent sources: Phase φ must be well defined and constant. When waves from coherent sources meet, stable interference can occur. Sunlight is coherent over a short length and time range. Since laser light is produced by cooperative behavior of atoms, it is coherent of long length and time ranges Incoherent sources: φ jitters randomly in time, no stable interference occurs 35-10

11 Intensity in Double-Slit Interference ( ) E1 = E0sin ωt and E = E0sin ωt+ φ E 1 1 π d I = 4I0 cos φ φ = sinθ π d 1 φ = mπ m = K φ = mπ = θ θ maxima when: for 0,1,, sin dsin = m for m= 0,1,, K (maxima) ( ) ( ) minima when: φ = m+ π dsin θ = m+ for m= 0,1,, K (minima) E I = I avg 0 Fig

12 Proof of Eqs. 35- and 35-3 Eq. 35- ( ) 0 ω 0 ( ω φ) = ( cos β) = 1 cos φ E t = E sin t+ E sin t+ =? E E E E = 4E cos φ I I E = = 4cos φ I = 4I cos E φ Fig β + β = φ Eq phase path length difference difference = π phase π path length difference = difference π φ = ( d sinθ) 35-1

13 In general, we may want to combine more than two waves. For eaxample, there may be more than two slits. Prodedure: Combining More Than Two Waves 1. Construct a series of phasors representing the waves to be combined. Draw them end to end, maintaining proper phase relationships between adjacent phasors.. Construct the sum of this array. The length of this vector sum gives the amplitude of the resulting phasor. The angle between the vector sum and the first phasor is the phase of the resultant with respect to the first. The projection of this vector sum phasor on the vertical axis gives the time variation of the resultant wave. E 4 E 3 E E 1 E 35-13

14 Interference from Thin Films φ 1 =? θ 0 Fig

15 Reflection Phase Shifts n 1 > n n 1 n n 1 < n Off lower index 0 Reflection Reflection Phase Shift n 1 n Off higher index 0.5 wavelength Fig

16 Fig Equations for Thin-Film Interference 0 Three effects can contribute to the phase difference between r 1 and r. 1. Differences in reflection conditions. Difference in path length traveled. 3. Differences in the media in which the waves travel. One must use the wavelength in each medium ( / n), to calculate the phase. ½ wavelength phase difference to difference in reflection of r 1 and r odd number odd number L = wavelength = n (in-phase waves) L = integer wavelength = integer n (out-of-phase waves) 1 L= m+ n for m= 0,1,, K (maxima-- bright film in air) n n L= m for m = 0,1,, K (minima-- dark film in air) n = ( )

17 Film Thickness Much Less Than r If L much less than l, for example L < 0.1, than phase difference due to the path difference L can be neglected. r 1 Phase difference between r 1 and r will always be ½ wavelength destructive interference film will appear dark when viewed from illuminated side

18 Color Shifting by Morpho Butterflies and Paper Currencies For the same path difference, different wavelengths (colors) of light will interfere differently. For example, L could be an integer number of wavelengths for red light but a half integer wavelengths for blue. Furthermore, the path difference L will change when light strikes the surface at different angles, again changing the interference condition for the different wavelengths of light. Fig

19 Problem Solving Tactic 1: Thin-Film Equations Equations and are for the special case of a higher index film flanked by air on both sides. For multilayer systems, this is not always the case and these equations are not appropriate. What happens to these equations for the following system? r r 1 L n 1 =1 n =1.5 n 3 =

20 Fig N m Michelson Interferometer L= d1 d (interferometer) Lm = L (slab of material of thickness L placed in front of M ) N m L Ln = = (number of wavelengths m in slab of material) L Na = (number of wavelengths in same thickness of air) Ln L L - Na= = ( n-1 ) (difference in wavelengths for paths with and without thin slab) For each change in path by 1, the interference pattern shifts by one fringe at T. By counting the fringe change, one determines N m - N a and can then solve for L in terms of and n

PH 222-3A Spring 2010

PH 222-3A Spring 2010 PH -3A Spring 010 Interference Lecture 6-7 Chapter 35 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 35 Interference The concept of optical interference is critical to understanding

More information

PS210 - Optical Techniques. Section VI

PS210 - Optical Techniques. Section VI PS210 - Optical Techniques Section VI Section I Light as Waves, Rays and Photons Section II Geometrical Optics & Optical Instrumentation Section III Periodic and Non-Periodic (Aperiodic) Waves Section

More information

Electricity & Optics

Electricity & Optics Physics 24100 Electricity & Optics Lecture 26 Chapter 33 sec. 1-4 Fall 2017 Semester Professor Koltick Interference of Light Interference phenomena are a consequence of the wave-like nature of light Electric

More information

1. Waves and Particles 2. Interference of Waves 3. Wave Nature of Light

1. Waves and Particles 2. Interference of Waves 3. Wave Nature of Light 1. Waves and Particles 2. Interference of Waves 3. Wave Nature of Light 1. Double-Slit Eperiment reading: Chapter 22 2. Single-Slit Diffraction reading: Chapter 22 3. Diffraction Grating reading: Chapter

More information

Physics General Physics II. Electricity, Magnetism and Optics Lecture 20 Chapter Wave Optics. Fall 2015 Semester Prof.

Physics General Physics II. Electricity, Magnetism and Optics Lecture 20 Chapter Wave Optics. Fall 2015 Semester Prof. Physics 21900 General Physics II Electricity, Magnetism and Optics Lecture 20 Chapter 23.1-2 Wave Optics Fall 2015 Semester Prof. Matthew Jones Announcement Exam #2 will be on Thursday, November 5 th (tomorrow)

More information

The Diffraction Grating

The Diffraction Grating The Diffraction Grating If one extends the double slit to large number of slits very closely spaced, one gets what is called a diffraction grating. d sin θ. Maxima are still at d sin θ m = mλ, m = 0, 1,

More information

Physical Optics 2018 Dr. Muwafaq Fadhil Al-Mishlab Third lecture [ Huygens Principle, Interference of light]

Physical Optics 2018 Dr. Muwafaq Fadhil Al-Mishlab Third lecture [ Huygens Principle, Interference of light] Physical Optics 2018 Dr. Muwafaq Fadhil Al-Mishlab Third lecture [ Huygens Principle, Interference of light] 1. Huygens principle Long before people understood the electromagnetic character of light, Christian

More information

Optics. n n. sin c. sin

Optics. n n. sin c. sin Optics Geometrical optics (model) Light-ray: extremely thin parallel light beam Using this model, the explanation of several optical phenomena can be given as the solution of simple geometric problems.

More information

Waves Part III Electromagnetic waves

Waves Part III Electromagnetic waves Waves Part III Electromagnetic waves Electromagnetic (light) waves Transverse waves Transport energy (and momentum) Can travel through vacuum (!) and certain solids, liquids and gases Do not transport

More information

The EYE. Physics 1502: Lecture 32 Today s Agenda. Lecture 4. Announcements: Optics. Midterm 2: graded after Thanks Giving

The EYE. Physics 1502: Lecture 32 Today s Agenda. Lecture 4. Announcements: Optics. Midterm 2: graded after Thanks Giving Physics 1502: Lecture 32 Today s Agenda Announcements: Midterm 2: graded after Thanks Giving Homework 09: Friday December 4 Optics Eye interference The EYE ~f o objective I 2 L I 1 ~f e eyepiece 1 2 Compound

More information

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : , 1 O P T I C S 1. Define resolving power of a telescope & microscope and give the expression for its resolving power. 2. Explain briefly the formation of mirage in deserts. 3. The radii of curvature of

More information

Some properties of waves: Huygens principle Superposition Coherence Interference Young s double-slit experiment Thin-film interference

Some properties of waves: Huygens principle Superposition Coherence Interference Young s double-slit experiment Thin-film interference Some properties of waves: Huygens principle Superposition Coherence Interference Young s double-slit experiment Thin-film interference Phys 2435: Chap. 35, Pg 1 Geometrical Optics Assumption: the dimensions

More information

WAVE OPTICS GENERAL. Fig.1a The electromagnetic spectrum

WAVE OPTICS GENERAL. Fig.1a The electromagnetic spectrum WAVE OPTICS GENERAL - The ray optics cannot explain the results of the two following experimental situations: a) When passing by small openings or illuminating small obstacles, the light bends around borders

More information

Physics for Scientists & Engineers 2

Physics for Scientists & Engineers 2 Light as Waves Physics for Scientists & Engineers 2 Spring Semester 2005 Lecture 41! In the previous chapter we discussed light as rays! These rays traveled in a straight line except when they were reflected

More information

Lecture PowerPoints. Chapter 24 Physics: Principles with Applications, 7 th edition Giancoli

Lecture PowerPoints. Chapter 24 Physics: Principles with Applications, 7 th edition Giancoli Lecture PowerPoints Chapter 24 Physics: Principles with Applications, 7 th edition Giancoli This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching

More information

Interference by Wavefront Division

Interference by Wavefront Division nterference by Wavefront Division One of the seminal experiments in physics was conducted in 1801 by Thomas Young, an English physicist who cut a small hole in an opaque screen, set a second screen in

More information

Double Slit is VERY IMPORTANT because it is evidence of waves. Only waves interfere like this.

Double Slit is VERY IMPORTANT because it is evidence of waves. Only waves interfere like this. Double Slit is VERY IMPORTANT because it is evidence of waves. Only waves interfere like this. Superposition of Sinusoidal Waves Assume two waves are traveling in the same direction, with the same frequency,

More information

LC circuit: Energy stored. This lecture reviews some but not all of the material that will be on the final exam that covers in Chapters

LC circuit: Energy stored. This lecture reviews some but not all of the material that will be on the final exam that covers in Chapters Disclaimer: Chapter 29 Alternating-Current Circuits (1) This lecture reviews some but not all of the material that will be on the final exam that covers in Chapters 29-33. LC circuit: Energy stored LC

More information

INTERFERENCE 1.1 NATURE OF LIGHT

INTERFERENCE 1.1 NATURE OF LIGHT 1 INTERFERENCE 1.1 NATURE OF LIGHT In the year 1678, Christian Huygens proposed the wave theory of light. According to this, a Luminous body is a source of disturbance in hypothetical medium called ether

More information

Chapter 10. Interference of Light

Chapter 10. Interference of Light Chapter 10. Interference of Light Last Lecture Wave equations Maxwell equations and EM waves Superposition of waves This Lecture Two-Beam Interference Young s Double Slit Experiment Virtual Sources Newton

More information

Lecture 4: Diffraction & Spectroscopy

Lecture 4: Diffraction & Spectroscopy Lecture 4: Diffraction & Spectroscopy d θ y L Spectra of atoms reveal the quantum nature of matter Take a plastic grating from the bin as you enter class. Lecture 4, p 1 Today s Topics Single-Slit Diffraction*

More information

Lecture 11: Introduction to diffraction of light

Lecture 11: Introduction to diffraction of light Lecture 11: Introduction to diffraction of light Diffraction of waves in everyday life and applications Diffraction in everyday life Diffraction in applications Spectroscopy: physics, chemistry, medicine,

More information

Lecture 9: Introduction to Diffraction of Light

Lecture 9: Introduction to Diffraction of Light Lecture 9: Introduction to Diffraction of Light Lecture aims to explain: 1. Diffraction of waves in everyday life and applications 2. Interference of two one dimensional electromagnetic waves 3. Typical

More information

Physics 102: Lecture 20 Interference. Physics 102: Lecture 20, Slide 1

Physics 102: Lecture 20 Interference. Physics 102: Lecture 20, Slide 1 Physics 102: Lecture 20 Interference Physics 102: Lecture 20, Slide 1 Phys 102 recent lectures Light as a wave Lecture 14 EM waves Lecture 15 Polarization Lecture 20 & 21 Interference & diffraction Light

More information

If the wavelength is larger than the aperture, the wave will spread out at a large angle. [Picture P445] . Distance l S

If the wavelength is larger than the aperture, the wave will spread out at a large angle. [Picture P445] . Distance l S Chapter 10 Diffraction 10.1 Preliminary Considerations Diffraction is a deviation of light from rectilinear propagation. t occurs whenever a portion of a wavefront is obstructed. Hecht; 11/8/010; 10-1

More information

Light as a Transverse Wave.

Light as a Transverse Wave. Waves and Superposition (Keating Chapter 21) The ray model for light (i.e. light travels in straight lines) can be used to explain a lot of phenomena (like basic object and image formation and even aberrations)

More information

Chapter 7. Interference of Light

Chapter 7. Interference of Light Chapter 7. Interference of Light Last Lecture Superposition of waves Laser This Lecture Two-Beam Interference Young s Double Slit Experiment Virtual Sources Newton s Rings Film Thickness Measurement by

More information

Michelson Interferometer

Michelson Interferometer Michelson Interferometer Objective Determination of the wave length of the light of the helium-neon laser by means of Michelson interferometer subsectionprinciple and Task Light is made to produce interference

More information

Phys 2310 Mon. Dec. 11, 2014 Today s Topics. Begin Chapter 9: Interference Reading for Next Time

Phys 2310 Mon. Dec. 11, 2014 Today s Topics. Begin Chapter 9: Interference Reading for Next Time Phys 30 Mon. Dec., 04 Todays Topics Begin Chapter 9: nterference Reading for Next Time Reading this Week By Wed.: Begin Ch. 9 (9. 9.3) General Considerations, Conditions for nterference, Wavefront-splitting

More information

1/d o +1/d i =1/f. Chapter 24 Wave Optics. The Lens Equation. Diffraction Interference Polarization. The Nature of Light

1/d o +1/d i =1/f. Chapter 24 Wave Optics. The Lens Equation. Diffraction Interference Polarization. The Nature of Light Chapter 24 Wave Optics Diffraction Interference Polarization 2F h o The Lens Equation 1/d o +1/d i =1/f F F O d o f d i h i Geometrical and Physical Optics Geometrical Optics: The study of optical phenomena

More information

Physics I : Oscillations and Waves Prof. S. Bharadwaj Department of Physics and Meteorology Indian Institute of Technology, Kharagpur

Physics I : Oscillations and Waves Prof. S. Bharadwaj Department of Physics and Meteorology Indian Institute of Technology, Kharagpur Physics I : Oscillations and Waves Prof. S. Bharadwaj Department of Physics and Meteorology Indian Institute of Technology, Kharagpur Lecture - 21 Diffraction-II Good morning. In the last class, we had

More information

Introduction to Condensed Matter Physics

Introduction to Condensed Matter Physics Introduction to Condensed Matter Physics Diffraction I Basic Physics M.P. Vaughan Diffraction Electromagnetic waves Geometric wavefront The Principle of Linear Superposition Diffraction regimes Single

More information

Week 7: Interference

Week 7: Interference Week 7: Interference Superposition: Till now we have mostly discusssed single waves. While discussing group velocity we did talk briefly about superposing more than one wave. We will now focus on superposition

More information

General Physics II Summer Session 2013 Review Ch - 16, 17, 18

General Physics II Summer Session 2013 Review Ch - 16, 17, 18 95.104 General Physics II Summer Session 2013 Review Ch - 16, 17, 18 A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positivecharged rod held near the ball. The

More information

Lecture 19 Optical MEMS (1)

Lecture 19 Optical MEMS (1) EEL6935 Advanced MEMS (Spring 5) Instructor: Dr. Huikai Xie Lecture 19 Optical MEMS (1) Agenda: Optics Review EEL6935 Advanced MEMS 5 H. Xie 3/8/5 1 Optics Review Nature of Light Reflection and Refraction

More information

Physics 280 Week 04 In-Class Problems Summer 2016

Physics 280 Week 04 In-Class Problems Summer 2016 Physics 80 Week 04 In-Class Problems Summer 016 1. Consider the interface of water with class (say at the bottom of a beaker filled with water). Given: The index of refraction for water is n w = 1.33 and

More information

Optics.

Optics. Optics www.optics.rochester.edu/classes/opt100/opt100page.html Course outline Light is a Ray (Geometrical Optics) 1. Nature of light 2. Production and measurement of light 3. Geometrical optics 4. Matrix

More information

Waves Part 3B: Interference

Waves Part 3B: Interference Waves Part 3B: Interference Last modified: 31/01/2018 Contents Links Interference Path Difference & Interference Light Young s Double Slit Experiment What Sort of Wave is Light? Michelson-Morley Experiment

More information

Physics 116. Nov 3, Lecture 21 Wave optics. R. J. Wilkes 11/3/11 1

Physics 116. Nov 3, Lecture 21 Wave optics. R. J. Wilkes   11/3/11 1 Physics 116 Lecture 21 Wave optics Nov 3, 2011 R. J. Wilkes Email: ph116@u.washington.edu 11/3/11 1 Announcements 3 clickers have quiz data logged, but no registration: 622961 649314 614235 If one of these

More information

PHYSICAL OPTICS. Ans: 1 Sol: The condition to form bright band at a point is to have a path difference of x = nλ From the given problem

PHYSICAL OPTICS. Ans: 1 Sol: The condition to form bright band at a point is to have a path difference of x = nλ From the given problem PHYSCAL OPTCS PREVOUS EAMCET BTS (ENGNEERNG PAPER). n the Young s doule slit experiment the intensities at two points P and P on the screen are respectively and. f P is located at the centre of right fringe

More information

OPSE FINAL EXAM Fall 2016 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT.

OPSE FINAL EXAM Fall 2016 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. CLOSED BOOK. Equation Sheet is provided. YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. ALL NUMERICAL ANSERS MUST HAVE UNITS INDICATED. (Except dimensionless units like

More information

REVISION: WAVES, SOUND & LIGHT 11 JUNE 2013

REVISION: WAVES, SOUND & LIGHT 11 JUNE 2013 REVISION: WAVES, SOUND & LIGHT 11 JUNE 2013 Lesson Description In this lesson we revise: the Doppler Effect, Huygens Principle, Diffraction of Light & the Photoelectric Effect Key Concepts The Doppler

More information

sin constructive n same condition destructive 2 Interference Constructive - Destructive 2-slit single slit diff. grating

sin constructive n same condition destructive 2 Interference Constructive - Destructive 2-slit single slit diff. grating Interference Constructive - Destructive 2-slit single slit diff. grating reflection Note: difference = 0 difference destructive 2 d sin reflection constructive d 2 sin tot. inter. = reflection + path length

More information

Andy Buffler Department of Physics University of Cape Town

Andy Buffler Department of Physics University of Cape Town University of Cape Town Department of Physics PHY014F Vibrations and Waves Part 3 Travelling waves Boundary conditions Sound Interference and diffraction covering (more or less) French Chapters 7 & 8 Andy

More information

Intensity of Interference Patterns

Intensity of Interference Patterns Intensity of Interference Patterns Wish to find I on a screen far away Let consider the E fields coming from the double slits: S 2 S 1 r r 2 1 E field from S 2 has a phase lag due to the extra path difference,

More information

Problem Set 5: Solutions

Problem Set 5: Solutions University of Alabama Department of Physics and Astronomy Department of Electrical and Computer Engineering PH 495/ECE 493 LeClair & Kung Spring 011 Problem Set 5: Solutions 1. Bekefi & Barrett 8.; Hecht

More information

Phys 2B Final Exam Name:

Phys 2B Final Exam Name: Phys 2B Final Exam Name: Multiple Choice (3 points each) 1. Two capacitors initially uncharged are connected in series to a battery, as shown. What is the charge on the top plate of C 1? a. 81 μc b. 18

More information

Physics 4C. Chapter 35: Conceptual Questions: 2, 8, 12 Problems: 9, 21, 25, 26, 39, 40, 55, 72, 82, 83, 93

Physics 4C. Chapter 35: Conceptual Questions: 2, 8, 12 Problems: 9, 21, 25, 26, 39, 40, 55, 72, 82, 83, 93 Physics 4C Solutions to Chapter 35 HW Chapter 35: Conceptual Questions:, 8, 1 Problems: 9, 1, 5, 6, 39, 40, 55, 7, 8, 83, 93 Question 35- (a) increase (b) 1λ Question 35-8 (a) 300 nm (b) exactly out of

More information

INTERFERENCE OF LIGHT

INTERFERENCE OF LIGHT INTERFERENCE OF LIGHT Physics Without Fear Want to be good in Physics? Remember: PHYSICS IS AN ACTIVE SPORT Physics is like a sport. To be good in a sport, you must practice. Likewise, to be good in Physics

More information

TA/TI survey. Phy Phy

TA/TI survey.   Phy Phy TA/TI survey https://webapps.pas.rochester.edu/secure/phpq/ Phy121 7 60 73 Phy123 1 6 11 Chapter 34 The Wave Nature of Light; Interference Units of Chapter 34 34-5 Interference in Thin Films 34-6 Michelson

More information

Waves Part 3: Superposition

Waves Part 3: Superposition Waves Part 3: Superposition Last modified: 06/06/2017 Superposition Standing Waves Definition Standing Waves Summary Standing Waves on a String Standing Waves in a Pipe Standing Waves in a Pipe with One

More information

Downloaded from

Downloaded from Question 10.1: Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected, and (b) refracted light? Refractive index

More information

Coherent vs. Incoherent light scattering

Coherent vs. Incoherent light scattering 11. Light Scattering Coherent vs. incoherent scattering Radiation from an accelerated charge Larmor formula Rayleigh scattering Why the sky is blue Reflected and refracted beams from water droplets Rainbows

More information

Concave mirrors. Which of the following ray tracings is correct? A: only 1 B: only 2 C: only 3 D: all E: 2& 3

Concave mirrors. Which of the following ray tracings is correct? A: only 1 B: only 2 C: only 3 D: all E: 2& 3 Concave mirrors Which of the following ray tracings is correct? A: only 1 B: only 2 C: only 3 D: all E: 2& 3 1 2 3 c F Point C: geometrical center of the mirror, F: focal point 2 Concave mirrors Which

More information

Lecture 15 Interference Chp. 35

Lecture 15 Interference Chp. 35 Lecture 15 Interference Chp. 35 Opening Demo Topics Interference is due to the wave nature of light Huygen s principle, Coherence Change in wavelength and phase change in a medium Interference from thin

More information

Interference, Diffraction and Fourier Theory. ATI 2014 Lecture 02! Keller and Kenworthy

Interference, Diffraction and Fourier Theory. ATI 2014 Lecture 02! Keller and Kenworthy Interference, Diffraction and Fourier Theory ATI 2014 Lecture 02! Keller and Kenworthy The three major branches of optics Geometrical Optics Light travels as straight rays Physical Optics Light can be

More information

TOPIC: LIGHT, ELECTROMAGNETIC WAVES, 2D AND 3D WAVEFRONTS

TOPIC: LIGHT, ELECTROMAGNETIC WAVES, 2D AND 3D WAVEFRONTS TOPIC: LIGHT, ELECTROMAGNETIC WAVES, 2D AND 3D WAVEFRONTS Learner Note: You need to know your definitions very well. You need to know the difference between refraction, reflection and diffraction. These

More information

Get Discount Coupons for your Coaching institute and FREE Study Material at RAY OPTICS - I

Get Discount Coupons for your Coaching institute and FREE Study Material at   RAY OPTICS - I RAY OPTICS - I 1. Refraction of Light 2. Laws of Refraction 3. Principle of Reversibility of Light 4. Refraction through a Parallel Slab 5. Refraction through a Compound Slab 6. Apparent Depth of a Liquid

More information

Chapter 35 Physical Optics: Light as a wave

Chapter 35 Physical Optics: Light as a wave Chapter 35 Physical Optics: Light as a wave Interference happens when two or more waves combine Examples of no-pigmented color presentation (iridescence): Beautiful oil spills Colors on soap bubble Color

More information

MIDTERM 3 REVIEW SESSION. Dr. Flera Rizatdinova

MIDTERM 3 REVIEW SESSION. Dr. Flera Rizatdinova MIDTERM 3 REVIEW SESSION Dr. Flera Rizatdinova Summary of Chapter 23 Index of refraction: Angle of reflection equals angle of incidence Plane mirror: image is virtual, upright, and the same size as the

More information

Optics. The refractive index of a material of a plain concave lens is 5/3, the radius of curvature is 0.3m. The focal length of the lens in air is ) 0.45 m ) 0.6 m 3) 0.75 m 4).0 m. The refractive index

More information

Interference. Gambar: Museum Victoria Australia

Interference. Gambar: Museum Victoria Australia Interference Gambar: Museum Victoria Australia Formulation of Interference Intensity Superposition between two waves (point sources) Two separate point sources S 1 (x 1 ) and S 2 (x 2 ) generate EM waves

More information

Engineering Physics 1 Prof. G.D. Varma Department of Physics Indian Institute of Technology-Roorkee

Engineering Physics 1 Prof. G.D. Varma Department of Physics Indian Institute of Technology-Roorkee Engineering Physics 1 Prof. G.D. Varma Department of Physics Indian Institute of Technology-Roorkee Module-03 Lecture-01 Interference of Light Part 01 Myself, Dr. JD Varma, Associate Professor in Department

More information

C. Incorrect! The velocity of electromagnetic waves in a vacuum is the same, 3.14 x 10 8 m/s.

C. Incorrect! The velocity of electromagnetic waves in a vacuum is the same, 3.14 x 10 8 m/s. AP Physics - Problem Drill 21: Physical Optics 1. Which of these statements is incorrect? Question 01 (A) Visible light is a small part of the electromagnetic spectrum. (B) An electromagnetic wave is a

More information

A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.

A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth. Waves_P2 [152 marks] A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth. The beam is incident normally on a double slit. The distance between the slits

More information

Tutorial 7: Solutions

Tutorial 7: Solutions Tutorial 7: Solutions 1. (a) A point source S is a perpendicular distance R away from the centre of a circular hole of radius a in an opaque screen. f the distance to the periphery is (R + l), show that

More information

UNIT-5 EM WAVES UNIT-6 RAY OPTICS

UNIT-5 EM WAVES UNIT-6 RAY OPTICS UNIT-5 EM WAVES 2 Marks Question 1. To which regions of electromagnetic spectrum do the following wavelengths belong: (a) 250 nm (b) 1500 nm 2. State any one property which is common to all electromagnetic

More information

Physics 142 Wave Optics 1 Page 1. Wave Optics 1. For every complex problem there is one solution that is simple, neat, and wrong. H.L.

Physics 142 Wave Optics 1 Page 1. Wave Optics 1. For every complex problem there is one solution that is simple, neat, and wrong. H.L. Physics 142 Wave Optics 1 Page 1 Wave Optics 1 For every complex problem there is one solution that is simple, neat, and wrong. H.L. Mencken Interference and diffraction of waves The essential characteristic

More information

Measurements in Optics for Civil Engineers

Measurements in Optics for Civil Engineers Measurements in Optics for Civil Engineers I. FOCAL LENGTH OF LENSES The behavior of simplest optical devices can be described by the method of geometrical optics. For convex or converging and concave

More information

Chapter 35 Diffraction and Polarization

Chapter 35 Diffraction and Polarization Chapter 35 Diffraction and Polarization If light is a wave, it will diffract around a single slit or obstacle. The resulting pattern of light and dark stripes is called a diffraction pattern. This pattern

More information

Engineering Physics 1 Prof. G.D. Vermaa Department of Physics Indian Institute of Technology-Roorkee

Engineering Physics 1 Prof. G.D. Vermaa Department of Physics Indian Institute of Technology-Roorkee Engineering Physics 1 Prof. G.D. Vermaa Department of Physics Indian Institute of Technology-Roorkee Module-04 Lecture-02 Diffraction Part - 02 In the previous lecture I discussed single slit and double

More information

Chapter 35 Diffraction and Polarization. Copyright 2009 Pearson Education, Inc.

Chapter 35 Diffraction and Polarization. Copyright 2009 Pearson Education, Inc. Chapter 35 Diffraction and Polarization 35-1 Diffraction by a Single Slit or Disk If light is a wave, it will diffract around a single slit or obstacle. 35-1 Diffraction by a Single Slit or Disk The resulting

More information

Some Topics in Optics

Some Topics in Optics Some Topics in Optics The HeNe LASER The index of refraction and dispersion Interference The Michelson Interferometer Diffraction Wavemeter Fabry-Pérot Etalon and Interferometer The Helium Neon LASER A

More information

Phys102 Lecture Diffraction of Light

Phys102 Lecture Diffraction of Light Phys102 Lecture 31-33 Diffraction of Light Key Points Diffraction by a Single Slit Diffraction in the Double-Slit Experiment Limits of Resolution Diffraction Grating and Spectroscopy Polarization References

More information

LECTURE 32: Young's Double-Slit Experiment

LECTURE 32: Young's Double-Slit Experiment Select LEARNING OBJECTIVES: LECTURE 32: Young's Double-Slit Experiment Understand the two models of light; wave model and particle model. Be able to understand the difference between diffraction and interference.

More information

The Quantum Theory of Atoms and Molecules

The Quantum Theory of Atoms and Molecules The Quantum Theory of Atoms and Molecules Breakdown of classical physics: Wave-particle duality Dr Grant Ritchie Electromagnetic waves Remember: The speed of a wave, v, is related to its wavelength, λ,

More information

Final Exam is coming!

Final Exam is coming! Final Exam is coming! Thurs., May 4, 4:30 to 6:30 pm, in this room. 25 multiple-choice questions Personalized exams I will enter the grade on your Mastering Physics account ( Final ). Old Part is comprehensive.

More information

The Quantum Theory of Atoms and Molecules: Waves and Optics. Hilary Term Dr Grant Ritchie

The Quantum Theory of Atoms and Molecules: Waves and Optics. Hilary Term Dr Grant Ritchie The Quantum Theory of Atoms and Molecules: Waves and Optics Hilary Term 008 Dr Grant Ritchie Wave motion - travelling waves Waves are collective bulk disturbances, whereby the motion at one position is

More information

Physics 30: Chapter 5 Exam Wave Nature of Light

Physics 30: Chapter 5 Exam Wave Nature of Light Physics 30: Chapter 5 Exam Wave Nature of Light Name: Date: Mark: /33 Numeric Response. Place your answers to the numeric response questions, with units, in the blanks at the side of the page. (1 mark

More information

Interference- Michelson Interferometer. Interference lecture by Dr. T.Vishwam

Interference- Michelson Interferometer. Interference lecture by Dr. T.Vishwam Interference- Michelson Interferometer Interference lecture by Dr. T.Vishwam * Measurement of the coherence length of a spectral line * Measurement of thickness of thin transparent flakes * Measurement

More information

Two-Source Constructive and Destructive Interference Conditions

Two-Source Constructive and Destructive Interference Conditions Two-Source Constructive and Destructive Interference Conditions Crests Crests Crests Crests ath length difference: l = - Travel time difference: t = t 2 - t 1 t = ( - )/v Crests Crests h 1 g 1 f 1 e 1

More information

CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter

CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter 1 Announcements Add to your notes of Chapter 1 Analytical sensitivity γ=m/s s Homework Problems 1-9, 1-10 Challenge

More information

CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter

CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter Announcements Add to your notes of Chapter 1 Analytical sensitivity γ=m/s s Homework Problems 1-9, 1-10 Challenge

More information

Contents. Diffraction by 1-D Obstacles. Narrow Slit. Wide Slit. N Slits. 5 Infinite Number of Slits

Contents. Diffraction by 1-D Obstacles. Narrow Slit. Wide Slit. N Slits. 5 Infinite Number of Slits Diffraction Contents 1 2 Narrow Slit 3 Wide Slit 4 N Slits 5 Infinite Number of Slits - geometric arrangement diffraction pattern amplitude Fk ( ) ik r F( k)= f( r) dr all r f( r) : amplitude function

More information

Interferometers. PART 1: Michelson Interferometer The Michelson interferometer is one of the most useful of all optical instru

Interferometers. PART 1: Michelson Interferometer The Michelson interferometer is one of the most useful of all optical instru Interferometers EP421 Lab Interferometers Introduction: Interferometers are the key to accurate distance measurement using optics. Historically, when mechanical measurements dominated, interferometers

More information

The University of Hong Kong Department of Physics

The University of Hong Kong Department of Physics The University of Hong Kong Department of Physics Physics Laboratory PHYS3551 Introductory Solid State Physics Experiment No. 3551-2: Electron and Optical Diffraction Name: University No: This experiment

More information

FIRST YEAR PHYSICS. Unit 4: Light II

FIRST YEAR PHYSICS. Unit 4: Light II FIRST YEAR PHYSICS Unit 4: Light II Contents PHASORS...3 RESOLUTION OF OPTICAL INSTRUMENTS...5 Rayleigh s criterion... 7 MORE ON DIFFRACTION...11 Multiple slits:... 11 Diffraction gratings... 14 X-RAY

More information

Electromagnetic Waves A.K.A. Light

Electromagnetic Waves A.K.A. Light Electromagnetic Waves A.K.A. Light When Thomas Edison worked late into the night on the electric light, he had to do it by gas lamp or candle. I'm sure it made the work seem that much more urgent. George

More information

IO3. Modul Optics. Diffraction

IO3. Modul Optics. Diffraction IO3 Modul Optics Diffraction The phenomenon of diffraction is an essential manifestation of the wave properties of light. As a part of geometrical optics, this phenomenon can not be understood because

More information

Physics 234 Homework Chapter 35 Q3, P3, P24, P32, P55, P81, P91. air

Physics 234 Homework Chapter 35 Q3, P3, P24, P32, P55, P81, P91. air Physics 34 Homework Chapter 35 Q3, P3, P4, P3, P55, P8, P9 Q a) r = r a r b = 5d 3d = d. b) r = /. c) / = d = r. Also, r = 3(/), 5(/), etc., works. d) / = d so d = /4. P3) (a) We take the phases of both

More information

The maximum value of the acceleration occurs when sin=1 with magnitude

The maximum value of the acceleration occurs when sin=1 with magnitude SOLUTIONS 1231 T1 Q1. SHM Vibrating Strip (a)(i) For SHM, y = Asin(ωt + φ ) for amplitude A and angular frequency ω. Set φ = 0. (ii) The velocity is given by v = dy dx = ωa cosωt The maximum speed vm occurs

More information

Modern Physics. Luis A. Anchordoqui. Department of Physics and Astronomy Lehman College, City University of New York. Lesson III September 3, 2015

Modern Physics. Luis A. Anchordoqui. Department of Physics and Astronomy Lehman College, City University of New York. Lesson III September 3, 2015 Modern Physics Luis A. Anchordoqui Department of Physics and Astronomy Lehman College, City University of New York Lesson III September 3, 2015 L. A. Anchordoqui (CUNY) Modern Physics 9-17-2015 1 / 23

More information

Diffraction I. Physics 2415 Lecture 37. Michael Fowler, UVa

Diffraction I. Physics 2415 Lecture 37. Michael Fowler, UVa Diffraction I Physics 2415 Lecture 37 Michael Fowler, UVa Today s Topics Michelson s interferometer The Michelson Morley experiment Single-slit diffraction Eye of a fly Angular resolution Michelson Interferometer

More information

9.4 Light: Wave or Particle?

9.4 Light: Wave or Particle? Huygens principle every point on a wave front can be considered as a point source of tiny secondary wavelets that spread out in front of the wave at the same speed as the wave itself rectilinear propagation

More information

and the radiation from source 2 has the form. The vector r points from the origin to the point P. What will the net electric field be at point P?

and the radiation from source 2 has the form. The vector r points from the origin to the point P. What will the net electric field be at point P? Physics 3 Interference and Interferometry Page 1 of 6 Interference Imagine that we have two or more waves that interact at a single point. At that point, we are concerned with the interaction of those

More information

Conceptual Practice Problems for PHYS 1112 In-Class Exam #2A+2B

Conceptual Practice Problems for PHYS 1112 In-Class Exam #2A+2B Conceptual ractice roblems for HYS 1112 In-Class xam #2A+2B Thu. Mar. 19, 2009, 11:00am-12:15pm and 2:00pm-3:15pm C 2.01: In a two-source interference experiment two sources are oscillating in phase with

More information

Fizeau s Interference Experiment with Moving Water Contradicts the Special Theory of Relativity.

Fizeau s Interference Experiment with Moving Water Contradicts the Special Theory of Relativity. Fizeau s Interference Experiment with Moving Water Contradicts the Special Theory of Relativity. Gennady Sokolov, Vitali Sokolov gennadiy@vtmedicalstaffing.com The interference experiment with moving water

More information

The science of light. P. Ewart

The science of light. P. Ewart The science of light P. Ewart Lecture notes: On web site NB outline notes! Textbooks: Hecht, Optics Lipson, Lipson and Lipson, Optical Physics Further reading: Brooker, Modern Classical Optics Problems:

More information

Physics 1C Lecture 14B. Today: End of Chapter 14 Start of Chapter 27

Physics 1C Lecture 14B. Today: End of Chapter 14 Start of Chapter 27 Physics 1C Lecture 14B Today: End of Chapter 14 Start of Chapter 27 ! Example Wave Interference! Two strings with linear densities of 5.0g/m are stretched over pulleys, adjusted to have vibrating lengths

More information

Atomic emission spectra experiment

Atomic emission spectra experiment Atomic emission spectra experiment Contents 1 Overview 1 2 Equipment 1 3 Measuring the grating spacing using the sodium D-lines 4 4 Measurement of hydrogen lines and the Rydberg Constant 5 5 Measurement

More information