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 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 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

5 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

6 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

7 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

8 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

9 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

10 CheckPoint 4 Two Polarizers Any non- horizontal polarizer azer 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

11 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

12 Q: How do we change the rela/ve phase between E x and E y? A: Birefringence 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

13 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

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

15 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

16 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

17 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

18 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

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

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

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

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

23 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: ShiZs phase of E field components in fast- slow direc/ons Strategic Analysis Determine state of polariza/on and intensity reduc/on azer each object Mul/ply individual intensity reduc/ons to get final reduc/on. Electricity & Magne/sm Lecture 24, Slide 22

24 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 azer 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 azer 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

25 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 azer the QWP? Before: A) I 2 = I 1 B) I 2 = ½ I 1 C) I 2 = ¼ I 1 No absorp/on: Just a phase change! I = 0 c h he 2 xi + heyi i 2 Same before & azer! AZer: Electricity & Magne/sm Lecture 24, Slide 24

26 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 azer the 60 o polarizer? A) LCP B) RCP C) D) x E) un- polarized Absorp/on: 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

27 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 azer 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

28 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 azer 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

29 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 azer the last QWP? I 3 = I 1 z Before: A) I 1 B) ½ I 1 C) ¼ I 1 No absorp/on: Just a phase change! Intensity = E 2 AZer: Electricity & Magne/sm Lecture 24, Slide 28

30 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 AZer first polarizer: LP along y axis with intensity I 1 AZer 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

31 Real Quarter Wave Plate Only shizs 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.

32 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

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