Electricity&Magnetism Lecture 24. Electricity & Magne/sm Lecture 24, Slide 1

Transcription

1 Electricity&Magnetism Lecture 24 Electricity & Magne/sm Lecture 24, Slide 1

2 Optics Kit Optics Bench Incandenscent Light Source Ray Table Ray Table Component Holder Component Holders (3) Slit Plate Ray Optics Mirror Slit Mask Cylindrical Lens Colour Filters: Parallel Ray Lens Crossed Arrow Target Viewing Screen Text Lenses: 75, 150 and 150 mm focal lengths Convex/Concave Mirror (±50 mm) DIFFRACTION GRATING 5276 LINES/cm Diffraction Grating red green blue-green Diffraction Scale Polarizers Virtual Image Locators Variable Aperture DIFFRACTION PLATE A B C D E DIFFRACTION PLATE J I H G F Diffraction Plate Figure 1: Equipment included in the OS-8500 Introductory Optics System

3 Lens or Mirror Polarizer Variable Aperture Figure 5: Using The Component Holder

4 from my favourite question-asker Lotsa questions, pick as many as you'd like Does a light wave have length / How long is one? How is a single light wave quantified? Is it a single or a stream of photons? Can you have light waves of different lengths? How long does it take for a light wave to be absorbed (Length of wave / C)? Can you split a light wave? (ie by absorbing half or something)? If a light wave has no length then couldn't you absorb the photon at a point when there is no energy? (at a node) Im confused by what polarizers actually do. Do they filter out light waves that aren't in a specific orientation or do they change the actual light waves' orientations? How come if you have linear polarizers in a series / - (0 degrees, 45 degrees, 90 degrees) Wouldn't the first polarizer only let the 0 degree oriented light through, then 45 will let even less, and 90 will let in only that which could pass through both the 45 and 0 degree polarizer?

5 So far we have considered plane waves that look like this: From now on just draw E and remember that B is s/ll there: Electricity & Magne/sm Lecture 24, Slide 3

6 Linear Polarization I was a bit confused by the introduction of the "e-hat" vector (as in its purpose/usefulness) Electricity & Magne/sm Lecture 24, Slide 4

7 Polarizer The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed. Electricity & Magne/sm Lecture 24, Slide 5

8 Clicker Question The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed. E o Suppose we have a beam traveling in the + z direc/on. At t = 0 and z = 0, the electric field is aligned along the posi/ve x axis and has a magnitude equal to E o y What is the component of E o along a direc/on in the x y plane that makes an angle of θ with respect to the x axis? Eo cosθ E o z A) E o sinθ B) E o cosθ C) 0 D) E o /sinθ E) E o /cosθ y θ Electricity & Magne/sm Lecture 24, Slide 6

9 I can't believe your teaching us the law of "Malus"(Malice). I thought malice was to be avoided? Electricity & Magne/sm Lecture 24, Slide 7

10 CheckPoint 2 Two Polarizers The second polarizer is orthogonal to the first No light will come through. cos(90 o ) = 0 Electricity & Magne/sm Lecture 24, Slide 8

11 CheckPoint 4 Two Polarizers Any non- horizontal polarizer a;er the first polarizer will produce polarized light at that angle Part of that light will make it through the horizontal polarizer Electricity & Magne/sm Lecture 24, Slide 9

12 There is no reason that φ has to be the same for E x and E y : Making φ x different from φ y causes circular or ellip<cal polariza<on: Example: At t = 0 RCP Electricity & Magne/sm Lecture 24, Slide 10

13 Q: How do we change the rela/ve phase between E x and E y? A: Birefringence Text Iceland Spar sun stone By picking the right thickness we can change the rela/ve phase by exactly 90 o. Right hand rule This changes linear to circular polariza/on and is called a quarter wave plate Electricity & Magne/sm Lecture 24, Slide 11

14 talk something about intensity NOTE: No Intensity is lost passing through the QWP! BEFORE QWP: AFTER THE SAME! Electricity & Magne/sm Lecture 24, Slide 12

15 Right or Left? red fox got it? Right circularly polarized Do right hand rule Fingers along slow direckon Cross into fast direckon If thumb points in direckon of propagakon: RCP Electricity & Magne/sm Lecture 24, Slide 13

16 Circular Light on Linear Polarizer Q: What happens when circularly polarized light is put through a polarizer along the y (or x) axis? A) I = 0 B) I = ½ I 0 C) I = I 0 X 1/2 Half of before Electricity & Magne/sm Lecture 24, Slide 14

17 CheckPoint 6 Case A Case B 50 Case A: E x is absorbed 38 Case B: (E x,e y ) phase changed Electricity & Magne/sm Lecture 24, Slide 15

18 Intensity: h I = 0 c he 2 xi + heyi 2 i PHASE QW Plate CHANGE Both E x and E y are s/ll there, so intensity is the same Electricity & Magne/sm Lecture 24, Slide 16

19 I = 0 c h he 2 xi + he 2 yi i ABSORB Polarizer COMPONENT E x is missing, so intensity is lower Electricity & Magne/sm Lecture 24, Slide 17

20 CheckPoint 8 Case A Case B /4 λ Z RCP Electricity & Magne/sm Lecture 24, Slide 18

21 CheckPoint 10 Case A Case B ½ λ 13 Z Z 0 1 Electricity & Magne/sm Lecture 24, Slide 19

22 Executive Summary: Polarizers & QW Plates: Polarized Light Circularly or Un- polarized Light Birefringence RCP Electricity & Magne/sm Lecture 24, Slide 20

23 Demo What else can we put in there to change the polarizakon? Electricity & Magne/sm Lecture 24, Slide 21

24 Bees Downloaded from on July 15, Phil. Trans. R. Soc. B (2011) 366, doi: /rstb Research Honeybee navigation: following routes using polarized-light cues P. Kraft1,3, C. Evangelista1,3, M. Dacke1,3,4, T. Labhart3,5 and M. V. Srinivasan1,2,3,* 1 Queensland Brain Institute, The University of Queensland, Saint Lucia, Queensland 4072, Australia School of Information Technology and Electrical Engineering, The University of Queensland, Saint Lucia, Queensland 4072, Australia 3 Australian Research Council Centre for Excellence in Vision Science, Australian National University, Canberra, ACT 2601, Australia 4 Department of Cell and Organism Biology, Lund University, Lund, Helgonovaagen, Sweden 5 Department of Neurobiology, Institute of Molecular Life Sciences, University of Zurich, Zurich, Switzerland 2 While it is generally accepted that honeybees (Apis mellifera) are capable of using the pattern of polarized light in the sky to navigate to a food source, there is little or no direct behavioural evidence that they actually do so. We have examined whether bees can be trained to find their way through a maze composed of four interconnected tunnels, by using directional information provided by polarized light illumination from the ceilings of the tunnels. The results show that bees can learn this task, thus demonstrating directly, and for the first time, that bees are indeed capable of using the polarized-light information in the sky as a compass to steer their way to a food source. Keywords: honeybee; navigation; polarization vision; orientation

25 Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. What is the intensity I 3 in terms of I 1? y x 45 o fast I 1 slow 60o I 2 I 3 z Conceptual Analysis Linear Polarizers: absorbs E field component perpendicular to Transmission Axis (TA) Quarter Wave Plate: Shi;s phase of E field components in fast- slow direckons Strategic Analysis Determine state of polarizakon and intensity reduckon a;er each object MulKply individual intensity reduckons to get final reduckon. Electricity & Magne/sm Lecture 24, Slide 22

26 Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. y x 45 o fast E 1 slow E x RCP E y 60o I 1 λ / 4 I 2 I 3 z What is the polariza/on of the light acer the QWP? y A) LCP B) RCP C) x D) x E) un- polarized y Light incident on QWP is linearly polarized at 45 o to fast axis LCP or RCP? Easiest way: Right Hand Rule: Light will be circularly polarized a;er QWP Curl fingers of RH back to front Thumb points in dir of propaga<on if right hand polarized. RCP Electricity & Magne/sm Lecture 24, Slide 23

27 Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. y x 45 o fast E 1 slow E x RCP E y 60o I 1 λ / 4 I 2 I 3 z What is the intensity I 2 of the light acer the QWP? Before: A) I 2 = I 1 B) I 2 = ½ I 1 C) I 2 = ¼ I 1 No absorpkon: Just a phase change! I = 0 c h he 2 xi + heyi i 2 Same before & a;er! A;er: Electricity & Magne/sm Lecture 24, Slide 24

28 Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. y x 45 o fast I 1 E 1 slow E x RCP E y 60o E 3 λ / 4 I 2 = I 1 I 3 z What is the polariza/on of the light acer the 60 o polarizer? A) LCP B) RCP C) D) x E) un- polarized AbsorpKon: only passes components of E parallel to TA (θ = 60 o ) y x y 60 o 60 o E y E o Ex Electricity & Magne/sm Lecture 24, Slide 25

29 Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. y x 45 o fast I 1 E 1 slow E x RCP E y 60o E 3 λ / 4 I 2 = I 1 I 3 = ½ I 1 z What is the intensity I 3 of the light acer the 60 o polarizer? A) I 3 = I 1 B) I 3 = ½ I 1 C) I 3 = ¼ I 1 E y E o Ex NOTE: This does not depend on θ! Electricity & Magne/sm Lecture 24, Slide 26

30 Follow-Up 1 Replace the 60 o polarizer with another QWP as shown. y x 45 fast o E slow I 1 λ / 4 RCP E x E y slow fast E y E 3 E x I 2 = I 1 I 3 z What is the polariza/on of the light acer the last QWP? y A) LCP B) RCP C) D) E) un- polarized x y x Easiest way: E fast is λ/4 ahead of E slow Brings E x and E y back in phase! Electricity & Magne/sm Lecture 24, Slide 27

31 Follow-Up 2 Replace the 60 o polarizer with another QWP as shown. y x 45 o fast E I 1 λ / 4 slow RCP E x E y slow E 3 fast Ey E x I 2 = I 1 What is the intensity I 3 of the light acer the last QWP? I 3 = I 1 z Before: A) I 1 B) ½ I 1 C) ¼ I 1 No absorpkon: Just a phase change! Intensity = E 2 A;er: Electricity & Magne/sm Lecture 24, Slide 28

32 Follow-Up 3 Consider light incident on two linear polarizers as shown. Suppose I 2 = 1/8 I 0 y x I 0 E 1 60 o E 2 I 1 I 1 = ½ I 0 I 2 = 1/8 I 0 z What is the possible polariza/on of the input light? A) LCP B) 45 o C) un- polarized A;er first polarizer: LP along y axis with intensity I 1 A;er second polarizer: LP at 60 o wrt y axis Intensity: I 2 = I 1 cos 2 (60 o ) = ¼ I 1 I 2 = 1/8 I 0 I 1 = ½ I 0 D) all of above E) none of above Electricity & Magne/sm Lecture 24, Slide 29

33 Real Quarter Wave Plate Only shics light exactly λ/4 for one wavelength. Typically calibrated for 598 nm, Na light Circular Polarizers only work perfectly at 598 nm. Other wavelengths produce ellip-cal polariza/on. If you look at white light, you see colour- changes when you rotate circular polarizers. Use a Green filter, to reduce this effect. (not perfect) Real- life λ/? material, birefringent material: cellophane, clear scotch tape.

34 E rotates counterclockwise as a func<on of <me E spirals clockwise as a func<on of z Text Figure 28.4: Left and right circular polarization. E rotates clockwise as a func<on of <me E spirals counterclockwise as a func<on of z Radio link 3D glasses

35 Circular Polarizer Puzzle Look at a mirror covered by a circular polarizer. Flip the polarizer. Explain what you see.

36 Today you will play around with the polariza/on filters. Con/nue on Friday. Friday s lecture will be on circular polariza/on so you may wish to do the circular polariza/on then. λ/4 and λ/2 plates only work perfectly at one wavelength causes some colour effects. Can use green filter to reduce the colour anomalies Acer you feel you understand polariza/on, we have magic towers with 4 light windows. You take your set of filters and try to iden/fy the polariza/on state from each window and fill in the Quiz. 5 points.

37 Name! Date!! Polarization Quiz! Tower: I II III IV! Determine the polarization of the light coming out of each of the ports. Put the answer number in the answer column and explain the basis for your answer under Rationale. If your answer is 2, linearly polarized, state the angle of the transmission axis from the vertical using the coordinate system shown below: 0, 90, +45 or 45. Partial credit will be given for identifying circularly polarized light, but with the wrong handedness. (The filters are not ideal, so the linear or circular states are not perfect. By linear we mean "nearly linear," by circular we mean "nearly circular." Look straight through the ports normal to the surface.) Port Rationale Answer A B C D Choose answers from the following list: 1.! Unpolarized light 2.! Linearly polarized light! (state angle θ: 0, 90, +45 or 45 ) 3.! Right circularly polarized light 4.! Left circularly polarized light 5.! Elliptically polarized light transmission! axis y θ x z, direction of propagation 6.! Mixture of linearly polarized and unpolarized light 7.! Mixture of circularly polarized and unpolarized light