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8/29/2016 1 PHYS 450 Fall Semester 2016 Lecture 02: Light Rays, The 8/29/2016 PHYS 450 Fall semester 2016 Lecture 02: Light Rays, the Reflection of Light and Mirrors Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 02 1 Mirrors - Historical Context One of the oldest commonly observed optical phenomena is reflection. Reflection: mirrors . water mirrors: surface of lake eons ago . obsidian (volcanic glass) about 6,000 B.C. in Anatolia . from polished copper in Mesopotamia and Egypt around 4000 to 3000 B.C. looking glasses discovered in Egyptian pyramids built circa 1900 BC. Reflection is the change in direction of a wavefront at an interface between two different media. Initial understanding built on empirical observations. Early Chinese, Greek, and Arabian philosophers develop the science of geometrical optics - a method of studying light as rays instead of waves (or particles). 2 1 8/29/2016 Interaction of light with matter visible IR I=Irradiance (Intensity) A T R I (W/m2) = R + T + A (conservation of energy) . Aluminum: Good reflectivity throughout optical and near-IR. Inexpensive. Three regimes: . Silver: Better reflectivity than Al if > 500 nm, but degrades under ambient •if RI, mirrors conditions (tarnishes) and dies in the blue. •if AI, filters and absorbers . Gold: Better reflectivity in the IR, but not so good in the optical. •if TI, lenses 3 Specular vs. diffuse reflection Specular Collimated Reflection light beam Smooth surface: specular reflection Collimated Diffuse light beam Reflection Rough surface: diffuse reflection 4 2 8/29/2016 Reflection of Light When viewed from above, light from a laser pointer reflects from a vertical mirror. Definitions . Incident light: the light striking the mirror . Normal line: a line perpendicular to the surface where the incident light hits the mirror. Forms the reference line for angle measurement. Angle of incidence θi: the angle between the incident beam and the normal line . Angle of reflection θr: the angle between θr the reflected beam and the normal line θi Top View, looking down Law of reflection θi= θr 5 The law of reflection is used to exploit the deflection of light in many ways Normal line New reflected ray Incident ray (fixed) Original -θ -θ reflected ray final initial Obstacle Establish sign convention for rotations: CW rotation is + CCW rotation is – Periscope Initially, incident light is deflected by +2 Mirror rotates through – θ Reflected light now rotates through +2(-θ) Change in angular deflection: +2(-θ) - 2 = -2θ Light rotated CCW by 2θ 6 3 8/29/2016 φ < 90° EXAMPLE rays cross each other • Two plane mirrors meet at an angle φ. Normal lines • A single ray reflects successively from incident both mirrors. ray • What is angle ? • How does depend on angle of incident reflected beam? ray a) Assume φ < 90° and that only two reflections, one from each mirror, take place. dihedral edge, dihedral angle 1. From ABC 2. From ABD 2212 12 22 2212 12 3. AtpointD 22 7 b) Assume φ > 90° and that only two reflections, one from each mirror, take place. 1. From ABC φ > 90° 12 θ 22 θ2 1 θ2 θ1 B A 12 φ 2. From ABD C 22 dihedral edge, 12 dihedral angle 2 12 β 2 D 8 4 8/29/2016 The Physics of Plane Mirrors Source of light Light ray specular reflection many rays 9 What the Penguin “sees” Θr ho hi Θi so si object distance image distance The penguin “sees” a virtual image. How are so, si and ho, hi related? Comment on notation s, s’ vs. so, si vs. p, q. 10 5 8/29/2016 For plane mirrors, the image distance equals the object distance, i.e. so=si planar mirror so si Real object, Virtual image 11 Left to Right Reversal in Plane Mirror Image? +90o Right (CW) handed “R” ℓ Left r handed “R” -90o (CCW) Plane mirror changes the path of a Transparent Image in light ray. plastic sign plane mirror Mirror also changes the handedness (parity) of reflected image (left- right reversal). Q: Why does top-bottom not reverse? A: Mirror does NOT reverse Left- What you see in images left-to-right or top-to- handed “R” mirror when you view bottom, but front-to-back. light reflected from When you write 12 one click mirror 6 8/29/2016 How to Eliminate Left to Right Reversal in a Mirror Image? Two plane mirrors at 90° to each other form a roof. Handedness=(-1)r=(-1)2=+1 A result of +1 indicates no change in the handedness (parity), while a result of -1 indicates θ θ a change in the 2 1 handedness (parity). B θ2 θ1 A φ φ =90° A roof is equivalent to a plane C mirror, except that the dihedral edge, handedness of reflected light is dihedral angle not changed. 13 Plane mirrors - summary • The image of the real object seen in a plane mirror is located where light reflected from the mirror to the eye of the observer seems to originate. • This perceived image is behind the mirror and not on the surface of the mirror. • Using ray diagrams, the image is exactly the same distance behind the plane mirror as the object is in front of it. • The image produced by a plane mirror is a virtual image – NO light actually comes from the image. 14 7 8/29/2016 Mirrors made from curved surfaces are more interesting Concave mirror Convex mirror R positive R negative Examples of curved mirrors 15 Definition of Terms: Two special points: C and F One special length: f=R/2 Center of curvature R Principal Axis Concave mirror Convex mirror focal length Focal Point f F=R/2 F=-R/2 16 8 8/29/2016 How are so, si and f related for concave mirror? PQC : PQF :2 2(1) Q specular QA reflection Θ so Point Θ QA object β α γ si × A C F QA P R R from (1) 112 Point image ssRoi distances si define fR / 2 so measured from A •s, s , and f are by definition positive 111 o i • can be extended to convex mirrors f ssoi (requires negative signs – see previous slides) • approximations becomes less accurate as 17 point object is moved off central axis Where is the Image? Ray Tracing for Concave Spherical Mirror three predictable rays: 1. parallel to Principal Axis 2. thru F Three predictable light rays; two important points 3. thru C specular reflection Theentireimageofanobject i can be deduced once a single ho r point on the image has been determined. hi specular s reflection One click i specular reflection so 111 hsii =+ m= =- magnification fssio hsoo 18 9 8/29/2016 Sign Conventions 111 Incident Incident f ss light oi light positive f, so, si negative si positive so negative f, si Concave mirror Convex mirror positive h i o , h , h o o o i i h positive negative negative h i o , h , h o i i h negative negative f=R/2 f=-R/2 19 Sign Conventions are Important (different textbooks may use different conventions) Curved Mirrors Quantity Symbol* Positive Sign means Negative Sign means Focal Length f Concave mirror Convex mirror Image si In front of mirror Behind mirror Distance (real) (virtual) Object so In front of mirror Behind mirror (virtual) Distance (real) Magnification m Image upright Image inverted Image Height hi Image upright Image inverted Be able to distinguish between Real and Virtual Images A negative or positive sign in front of a numerical value is used to represent information about direction. *each symbol can be assigned either + or – value. 20 10 8/29/2016 Systematics: Object-Image Locations for Convex Mirror Case 1 Case 2 Case 3 Case 4 object located beyond object located at center object located between object located at center of curvature (C) of curvature (C) center of curvature (C) and focal point (F) the focal point (F) Case 5 object located between focal point (F) and surface of mirror 21 Object-Image Locations for a Concave Mirror Different object locations are drawn in red and labeled with a number; the corresponding image locations are drawn in blue and labeled with the identical number. 6 images real objects 7 image at 8 12345678 C F 9 9 1 3 2 Concave 4 mirror images 5 Real image Virtual image http://www.physicsclassroom.com/ 22 11 8/29/2016 Object-Image Locations for a Convex Mirror Different object locations are drawn in red and labeled with a number; the corresponding image locations are drawn in blue and labeled with the identical number. objects 12345 images C 6 6 4 2 F Convex mirror real objects virtual images 23 Parabolic Mirrors Advantage Parabolic surface 24 12 8/29/2016 Aspherical Mirrors – any mirror surface not shaped like a sphere Off-axis mirrors Central axis 25 Up Next – Bending of Light (Refraction) and Thin Lenses 26 13 8/29/2016 APPENDIX A: Don’t be confused by the notation – different books use different symbols for the same thing Confusing Less Confusing 11 1 s sf' 11 1 oi f 111 soisf 11 1 pq f q p 27 Appendix B: A few worked out examples 28 14 8/29/2016 Example I: Concave Mirror on Floor in European Cathedrals Enlarged image of artwork on Concave mirror ceiling dome Object (cathedral artwork on ceiling) is located between center of curvature (C) and the focal point (F) of concave mirror. Real image that is inverted and magnified (case 5). 29 Example II: Convex mirror Gazing Globe A gazing globe has a diameter of 12 inches. If a bird that is 6 inches tall stands 36 inches in front of the globe, what will the bird see? Convex mirror R diameter =12 in specular R reflection f=- =-3in 2 Not to scale 111 =+ fssio hsii-2.77 111 1 1 121 13 m= =- =- =+0.23 uprightimage =- = - =-- =- hsoo 12 sfs-336363636io hi 0.23= hio =0.23h =0.23(6 in)=1.38in si = -2.77 in (virtual image,behind mirror) h o 30 15 8/29/2016 Example III: Concave mirror Butters stands 1 m in front of a concave mirror that has a radius of curvature of 1 m.
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