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SP Lecture 24 Electricity&Magnetism Lecture 24 Electricity & Magne/sm Lecture 24, Slide 1 Physics 131 Laboratory Manual Equipment Note: The Pasco Introductory Optics System Figure 1 shows all the equipment in the OS-8500 Introductory Optics System. The system also includes a fitted box with cutouts for each component. Please replace all components in their places after each lab period before returning the box. Optics Kit Optics Bench Incandenscent Light Source Ray Table Component Holder Ray Table Component Holders (3) Slit Plate Slit Mask Parallel Ray Lens Viewing Ray Optics Screen Lenses: 75, 150 and Mirror –150 mm focal lengths Crossed Convex/Concave Cylindrical Lens Arrow Mirror (±50 mm) Target DIFFRACTION GRATING 5276 LINES/cm Diffraction Colour Filters: Grating DIFFRACTION PLATE red A B C D E Diffraction Plate .. ... .. .. .. .. ..................... .. .. ... .. .. .. .... .. ..................... ... .. ... ..................... .. ..................... ... ... .. ..................... .. ..................... .. ..................... J I H G F G H I J green Virtual Image PLATE DIFFRACTION Diffraction Scale Locators blue-green Variable Polarizers Aperture Figure 1: Equipment included in the OS-8500 Introductory Optics System OP0.2 Physics 131 Laboratory Manual Component Holders The optics set comes with three regular component holders Centring Notch (Fig. 4) and one holder designed for use with the ray table. The regular component holders attach magnetically to the optics bench as in Figure 5. The ray table holder sits on the edge of the circular ray table. The notch at the top of each holder is for centring components on the holder. The notches in the base of the regular holders are for accurate distance measurements on the bench scale. Base Position Notch Figure 4: Component holder Variable Aperture Polarizer Lens or Mirror Figure 5: Using The Component Holder Top View Vertical Axes of Lens or Mirror Figure 6: Component Alignment OP0.4 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 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 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 Clicker Question The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed. Eo Suppose we have a beam traveling in the + z direcon. At t = 0 and z = 0, the electric field is aligned along the posi/ve y x axis and has a magnitude equal to Eo z What is the component of Eo along a direc/on in the x − y plane that makes an angle of θ with respect to the x − axis? E Eo o cos θ θ A) Eosinθ B) Eocosθ C) 0 D) Eo/sinθ E) Eo/cosθ y Electricity & Magne/sm Lecture 24, Slide 6 “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 CheckPoint 2 Two Polarizers 60 45 30 15 0 1 The second polarizer is orthogonal to the first No light will come through. cos(90o) = 0 Electricity & Magne/sm Lecture 24, Slide 8 CheckPoint 4 Two Polarizers 80 60 40 20 0 1 Any non-horizontal polarizer aer 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 There is no reason that φ has to be the same for Ex and Ey: Making φx different from φy causes circular or ellip/cal polarizaon: Example: At t = 0 RCP Electricity & Magne/sm Lecture 24, Slide 10 Q: How do we change the relave phase between Ex and Ey? A: Birefringence By picking the right thickness we can change the relave phase by exactly 90o. This changes linear to Right circular polarizaon hand rule and is called a quarter wave plate Electricity & Magne/sm Lecture 24, Slide 11 “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 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 propagaon: RCP Electricity & Magne/sm Lecture 24, Slide 13 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 I0 C) I = I0 X Half of before 1/2 Electricity & Magne/sm Lecture 24, Slide 14 CheckPoint 6 Case A Case B 50 38 Case A: Case B: 25 E x is absorbed (Ex ,Ey) phase changed 13 0 1 Electricity & Magne/sm Lecture 24, Slide 15 Intensity: I = ✏ c E2 + E2 0 h xi h y i h i PHASE QW Plate CHANgE Both Ex and Ey are s/ll there, so intensity is the same Electricity & Magne/sm Lecture 24, Slide 16 I = ✏ c E2 + E2 0 h xi h y i h i ABSORB Polarizer COMPONENT Ex is missing, so intensity is lower Electricity & Magne/sm Lecture 24, Slide 17 CheckPoint 8 Case AA Case BB 40 30 20 RCP 10 1/4 λ Z 0 1 Electricity & Magne/sm Lecture 24, Slide 18 CheckPoint 10 Case A Case B 50 38 25 ½ λ 13 Z Z 0 1 Electricity & Magne/sm Lecture 24, Slide 19 Executive Summary: Polarizers & QW Plates: Polarized Light Circularly or Un-polarized Light Birefringence RCP Electricity & Magne/sm Lecture 24, Slide 20 Demo What else can we put in there to change the polarizaon? Electricity & Magne/sm Lecture 24, Slide 21 Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. What is the intensity I3 in terms of I1? 45o fast y x slow 60o I1 I2 z I3 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 polarizaon and intensity reduc/on aer each object Mul/ply individual intensity reduc/ons to get final reduc/on. Electricity & Magne/sm Lecture 24, Slide 22 Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast y 45o E RCP x 1 slow Ex Ey 60o I1 λ / 4 I 2 z I3 What is the polarizaon of the light aer the QWP? y y A) LCP B) RCP C) x D) x E) un-polarized Light incident on QWP is linearly Light will be circularly polarized at 45o to fast axis polarized aer QWP LCP or RCP? Easiest way: Curl fingers of RH back to front Right Hand Rule: Thumb points in dir of propagaon RCP if right hand polarized. Electricity & Magne/sm Lecture 24, Slide 23 Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast y 45o E RCP x 1 slow Ex E y 60o I1 λ / 4 I 2 z I3 What is the intensity I2 of the light aer the QWP? A) I2 = I1 B) I2 = ½ I1 C) I2 = ¼ I1 Before: No absorp/on: Just a phase change! Aer: I = ✏ c E2 + E2 0 h xi h y i Same before & aer!h i Electricity & Magne/sm Lecture 24, Slide 24 Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast y 45o E RCP x 1 slow Ex E y 60o E3 I1 λ / 4 I2 = I1 z I3 What is the polarizaon of the light aer the 60o polarizer? y y 60o 60o A) LCP B) RCP C) D) E) x x un-polarized Absorp/on: only passes components of E parallel to TA (θ = 60o) E y 3 E3 60o Ex Electricity & Magne/sm Lecture 24, Slide 25 Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast y 45o E RCP x 1 slow Ex E y 60o E3 I1 λ / 4 I2 = I1 I3 = ½ I1 z o What is the intensity I3 of the light aer the 60 polarizer? A) I3 = I1 B) I3 = ½ I1 C) I3 = ¼ I1 E y 3 E3 60o NOTE: This does not depend on θ ! Ex Electricity & Magne/sm Lecture 24, Slide 26 Follow-Up 1 Replace the 60o polarizer with another QWP as shown. o fast y 45 RCP x E slow slow Ex Ey E3 I fast E 1 Ey x λ / 4 I = I 2 1 I3 z What is the polarizaon of the light aer the last QWP? y y A) LCP B) RCP C) D) E) x x un-polarized Easiest way: Brings Ex and Ey back in phase! Efast is λ/4 ahead of Eslow Electricity & Magne/sm Lecture 24, Slide 27 Follow-Up 2 Replace the 60o polarizer with another QWP as shown. o fast y 45 RCP x E slow slow Ex Ey E3 I fast E 1 Ey x λ / 4 I2 = I1 z I3 = I1 What is the intensity I3 of the light aer the last QWP? A) I1 B) ½ I1 C) ¼ I1 Before: No absorp/on: Just a phase change! Aer: Intensity = 〈E2〉 Electricity & Magne/sm Lecture 24, Slide 28 Follow-Up 3 Consider light incident on two linear polarizers as shown. Suppose I2 = 1/8 I0 y E x 1 60o E2 I0 I1 I2 = 1/8 I0 z I1 = ½ I0 What is the possible polarizaon of the input light? A) LCP AZer first polarizer: LP along y−axis with intensity I1 B) AZer second polarizer: LP at 60o wrt y−axis 45o 2 o Intensity: I2 = I1cos (60 ) = ¼ I1 C) un-polarized I2 = 1/8 I0 ⇒ I1 = ½ I0 D) all of above E) none of above Electricity & Magne/sm Lecture 24, Slide 29 Real Quarter Wave Plate •Only shiZs light exactly λ/4 for one wavelength.
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