Physics 1230: Light and Color. Projects
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1 Physics 1230: Light and Color Chuck Rogers, Matt Heinemann, Exam 2 tomorrow, here. HWK 6 is due at 5PM Thursday. Projects First list of proposed project topics and group members is due Friday. 1
2 Physics 1230: Light and Color Chuck Rogers, Matt Heinemann, Lecture 8 Spherical curved mirrors and their images. HWK 6 is due at 5PM Thursday. Exam 2 on Wed. 2
3 Flat-mirror images Flat mirrors find many uses due to their ability to show us images. The image is behind the mirror or just as far inside mirror land as the object is outside the mirror.
4 Image in a vertical mirror 1. If a point on the object is distance X in front of the mirror, the same point in the image appears to be distance X in back of the mirror, or X object = X image. 2. The image point is on the normal (extended) from the object to the mirror. Mirror normal extended X object X image 4
5 Ray tracing: Draw the image, then the rays First: draw rays from image to eyes Viewed from the side. Mirror X object X image 5
6 Ray tracing: Draw the image, then the rays First: draw rays from image to eyes Second: draw rays from mirror to object Mirror X object X image q i = q r happens automatically using this method. 6
7 Right side up image? The top ray goes to the top of the bottle. It is right side up. Mirror X object X image q i = q r happens automatically using this method. 7
8 Image from a horizontal mirror The top ray goes to the bottom of the bottle. It is upside down. X object Extension Mirror (to do this drawing, the mirror must be extended) X image q i = q r happens automatically using this method. 8
9 Bottle on its side Viewed from the side. Mirror (to do this drawing, the mirror must be extended) q i = q r happens automatically using this method. 9
10 For simple (flat) mirrors the image location is therefore predictable without knowing where the observer's eye is and without ray-tracing Mirror Mirror Mirror Mirror
11 The image of the bottle in the lower mirror is: A) Inverted B) Not inverted C) Something else Periscope mirror Original OBJECT mirror 11
12 Periscope? The first IMAGE extension Original OBJECT 12
13 Periscope? extension The second IMAGE 13
14 The image of the bottle in the lower mirror is: A) Inverted B) Not inverted C) Something else Periscope? 14
15 Corner reflector
16 Corner reflector Moon
17 Half-Silvered mirror If the silver coating is thin enough the mirror can be made to transmit 50% of the light and to reflect the other 50% This is called a half-silvered mirror A half-silvered mirror used with proper lighting can show objects on one side or the other of the mirror
18 One-way mirror How can you tell you are being spied upon?
19 Review: Plane mirrors make a VIRTUAL image OBJECT REFLECTED, VIRTUAL IMAGE Object distance Image distance Virtual image = rays appear to have come from where the image is, but they actually didn t. In this case, they bounced off the mirror.
20 Curved mirrors Convex: Make something smaller Lets you see a wide angle Bike mirrors, car mirrors Concave: Make something bigger You can t see much around you Image flips when get closer Makeup mirrors
21 Concave Convex versus vs concave convex spherical mirrors Spher ical mir rors are drawn in t wo dimensions, so you have t o imagine t he 3D mir ror t hat t his line represent s Bot h convex and concave mir rors obey t he same law of refl ect ion, but t hey make different kinds of images Convex# Concave#
22 Geometry review This line segment (from center of circle)......is perpendicular (or normal) to this tangent. 22
23 Ray tracing practice Do the ray tracing yourself along with me. The act of drawing the lines to practice is very important. If you haven t used a straight edge thus far now is a good time to start. With curved mirrors (and later lenses) very hard to get right unless you draw the lines straight. You have two copies of the same thing we ll do two separate exercises.
24 Rays reflecting from a convex (spherical) mirror Rays aimed toward center of sphere come straight back (specular reflection with normal incidence) C What about other rays? All rays aimed at the center C come straight back out. 24
25 What happens to all rays that come in parallel to the OPTICAL AXIS (the line running through C)? Specular reflection Find where incoming ray hits mirror surface Find surface normal at that point (along line from center--remember geometry review?) Angle of incidence = angle of reflection Reflection (of parallel ray) looks like it s coming from F -- turns out this is true for all parallel rays! q i q r F C The focus is halfway to the center 25
26 What happens to all rays that come in parallel? Focal point = focus is behind the surface Easy rule for parallel incoming rays (parallel to the line through F and C): they are reflected as if they came from F. F C The focus is halfway to the center 26
27 What about rays aimed at the focus? (This is the previous rule, backwards) Easy rule for rays aimed at focus: An incoming ray aimed at F gets reflected back parallel (to the C-F axis). Focal point = focus is behind the surface F C The focus is halfway to the center 27
28 Review: Rules for convex spherical mirrors 1. All rays incident parallel to the C- F axis are reflected so that they appear to be coming from the focal point F 2. All rays that (when extended) pass through the center C are reflected back on themselves. 3. All rays that (when extended) pass through the focal point F are reflected back parallel to the axis F C 28
29
30 Ray tracing: convex mirror What does the observer see in the mirror? F C 30
31 Ray tracing: convex mirror What does the observer see in the mirror? Draw in the rays and extrapolate back F 31 C
32 Ray tracing: convex mirror (A) Or (B)?? Is the image real or virtual? Is the image larger or smaller than the object? Is the image right-side-up or upsidedown? How could a mirror be useful when used like this? F 32 C
33
34 Position of focal point
35 Rays reflecting from concave (cavity) mirrors Ray through the center reflects straight back at its source C 35
36 Incoming parallel rays reflect through focus All (incoming parallel) rays reflect and go through the focus, about half way from center to mirror C F As usual, this rule works backwards: incoming rays that go through the focus reflect back parallel (to the C-F axis). 36
37 Rays through focus reflect back parallel to C-F axis. C F 37
38 Rules for concave spherical mirror 1. All rays incident parallel to the C-F axis are reflected through the focal point F. 2. All rays that pass through the center C are reflected back on themselves. 3. All rays that pass through the focal point F are reflected back parallel to the axis (reserve of rule 1) C F 38
39 Ray tracing: concave mirror object outside center C F 39
40 Concave mirror: Object outside center Smaller Upside-down C F (A) Or (B)? Is the image real or virtual? 40
41 Ray tracing: concave mirror object between center and focus C F (A) Or (B)? Is the image larger or smaller than the object? Is the image right-side-up or upside-down? Is the image real or virtual? 41
42 Ray tracing: concave mirror object between focus and mirror C F 42
43 Ray tracing: concave mirror object between focus and mirror C F (A) Or (B)? Is the image real or virtual? 43
44 Demos: Spoons Mirrors in front of room
45 Many distinct cases Convex spherical mirror Concave spherical mirror, object outside center Concave spherical mirror, object between center and focus Concave spherical mirror, object between focus and mirror For each case, you can now answer: Image larger? Virtual? Where? What good is it? AND you can answer these question by ray tracing with three (simple) rules
46 Application of concave mirror Application of concave mirrors focus sun s rays at a focal point F t o convert int o heat!
47 Application of concave mirror Application of concave mirrors light beam emit t er (fl ashlight ) - > produces collimat ed light What if we put a light source at t he focal point of a concave mir ror? All t he rays emit t ed go t hrough t he focal point, and are t herefore refl ect ed parallel t o t he axis of t he mir ror - > flashlight
48 Good place for a break
49 Physics 1230: Light and Color Chuck Rogers, Matt Heinemann, Exam 2 tomorrow, here. HWK 6 is due at 5PM Thursday. Projects First list of proposed project topics and group members is due Friday. 67
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