PHYS 219 Spring semester 2016 Lecture 19: Mirrors Ron Reifenberger Birck Nanotechnology Center Purdue University PHYS 219 Test II Wednesday; March 30, 2016 6:30 PM PHYS 203 Lecture 19 1
a) Interaction of light with matter I=Irradiance (Intensity) R A T b) EM radiation (light) travels slower in a material: n=c/v c= speed of light in vacuum (air) v=speed of light in a material I (W/m 2 ) = R + T + A (conservation of energy) Three regimes: if R I, mirrors if A I, filters and absorbers if T I, lenses material n glass 1.5 water 1.33 diamond 2.4 2
The Physics of Plane Mirrors Source of light Light ray specular reflection many rays 3
What the Penguin sees h o Θ r Θ i h i s o object distance s i image distance The penguin sees a virtual image. How are s o, s i and h o, h i related? Comment on notation s, s vs. s o, s i vs. p, q. 4
For plane mirrors, the image distance equals the object distance, i.e. s o =s i planar mirror s o s i Real object, Virtual image 5
Seeing an image in a plane mirror for the first time can be a mind-boggling experience Six month old infant 6
Left to Right Reversal in Plane Mirror Image? r l Plane mirror Transparent sign one click What you see when you view the sign in the mirror When you write 7
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. 8
Mirrors made from curved surfaces are more interesting Concave mirror Convex mirror R positive R negative Examples of curved mirrors 9
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 10
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 The entire image of an object can be deduced once a single point on the image has been determined. One click h o s o i r h i s i specular reflection specular reflection specular reflection See Appendix for derivation 1 1 1 = + f s s i o h i m= =- h o s s i o magnification 11
Sign Conventions Incident light Incident light positive f, s o, s i negative s i positive s o, s i negative f, s i Concave mirror Convex mirror positive h o, h i negative h o, h i o i o i positive negative h o, h h i o, h i f=r/2 f=-r/2 12
Quantity Symbol* Positive Sign means Negative Sign means Focal Length f Concave mirror Convex mirror Image Distance Object Distance Sign Conventions are Important (different textbooks may use different conventions) s i s o Curved Mirrors In front of mirror (real) In front of mirror (real) Behind mirror (virtual) Behind mirror (virtual) Magnification m Image upright Image inverted Image Height h i 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 a + or value. 13
Concave Mirror: A Systematic Summary Five (5) generic locations of an OBJECT: Case 1: the object is located beyond the center of curvature (C) Case 2: the object is located at the center of curvature (C) Case 3: the object is located between the center of curvature (C) and the focal point (F) Case 4: the object is located at the focal point (F) Case 5: the object is located between the focal point (F) and the mirror s surface http://www.physicsclassroom.com 14
Schematic: Object-Image Locations Case 1 Case 2 Case 3 object located beyond center of curvature (C) object located at center of curvature (C) Case 4 Case 5 object located between center of curvature (C) and the focal point (F) object located at focal point (F) object located between focal point (F) and surface of mirror 15
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. real objects images 7 6 image at 1 2 3 4 5 6 7 8 9 9 8 5 C 3 4 images 2 1 F Concave mirror Real image Virtual image http://www.physicsclassroom.com/ 16
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 1 2 3 4 5 6 images 6 4 2 F C Convex mirror real objects virtual images 17
Example I: Concave Mirror in European Cathedrals Concave mirror Enlarged image of artwork on 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. 18 one click
Example II: Two parabolic mirrors separated by one focal length 19
Example III: Focusing heat radiation R R concave mirror object F C C image F 20
Example IV: 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 R f=- =-3in 2 1 1 1 = + f si so 1 1 1 1 1 12 1 13 = - = - =- - =- si f so -3 36 36 36 36 s = -2.77 in (virtual image,behind mirror) i hi s -2.77 i m= =- =- =+0.23 uprightimage ho so 12 hi 0.23 = h i = 0.23 h o = 0.23(6 in) =1.38 in h 21 o specular reflection Not to scale
Example V: Concave mirror Butters stands 1 m in front of a concave mirror that has a radius of curvature of 1 m. Where is his image formed? object radius of curvature = 1 m concave mirror C F radius = +1.0 m R f=+ =+0.5 m 2 1 1 1 = + f si so 1 1 1 1 1 = - = - =2.0-1.0 = +1.0 s f s +0.5 1.0 i i o s = +1.0 m (realimage,in front of mirror) image h hi -1.0 = h i = -h h i i m= =- =- =-1.0 invertedimage o o s o 1.00 h s 1.00 o 22
Up Next Thin Lenses 23
APPENDIX A: Derivation of the Curved Mirror Equation from Euclid: the sum of opposite interior angles equals the exterior angle Q P α R γ or + = 24
How are s o, s i and f related for concave mirror? from Euclid: the sum of opposite interior angles equals the exterior angle PQC : PQF : 2 2 (1) QA so QA si QA R from (1) 1 1 2 so si R define f R/ 2 Point object P 1 1 1 f s s o α i R s o s o, s i, and f are by definition positive can be extended to convex mirrors (requires negative signs see previous slides) becomes less accurate as point object is moved off central axis C γ Θ Θ β F Q s i specular reflection A distances measured from A 25
Don t be confused by the notation different books use different symbols for the same thing 1 1 1 s s' f p q 1 1 1 p q f 26
APPENDIX B: Run Simulations http://physics.bu.edu/~duffy/java/opticsa1.html 27