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Exam

Exam. The second exam in Physics 104 is on Thursday, March 24 from 5:45 - 7:00 PM . Rooms are same as Exam 1: Sections 303, 315, 316, 319, 320, 325(TAs Asgar, Geng, Yip) meet in B102 Van Vleck

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Exam

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  1. Exam • The second exam in Physics 104 is on Thursday, March 24 from 5:45 - 7:00 PM. • Rooms are same as Exam 1: • Sections 303, 315, 316, 319, 320, 325(TAs Asgar, Geng, Yip) meet in B102 Van Vleck • Sections 301, 304, 305, 306, 307, 309, 313, 314, 324(TAs Belknap, Hinojosa, Walker) meet in 3650 Humanities Sections 302, 310, 311, 312, 317, 318, 321, 322, 323 (TAs Dai, Hostetter, Ojalvo ) meet in B10 Ingraham • The exam will cover chapters 19-22. Physics 104, Spring 2010

  2. Mirrors • Mirrors • Plane (Flat) • Spherical • Converging (Concave) • Diverging (Convex) • Radius of Curvature / Focal length • Image Position, Magnification and Type Physics 104, Spring 2010

  3. Flat Mirror θf d Draw first ray perpendicular to mirror 0 = θi = θf Draw second ray at angle. θi = θf Lines appear to intersect a distance d behind mirror. This is the image location. Virtualimage since light rays don’t really converge. All rays originating from peak will appear to converge at same point behind mirror! Virtual: No light actually gets here θi d Physics 104, Spring 2010

  4. Plane Mirror Summary d • Image is: • Upright(Inverted) • Same size (magnified) • Located same distance from, but behind, mirror (image distance) • Facing opposite direction: Left/Right reversed • Virtual: (real image) d Physics 104, Spring 2010

  5. Flat Mirror Question You are standing in front of a short flat mirror which is placed too high, so you can see above your head, but only down to your knees. To see your shoes, you must move • closer to the mirror. • further from the mirror. • to another mirror. Changing distance doesn’t change what you see of yourself Physics 104, Spring 2010

  6. Curved mirrors Concave mirror R R Convex mirror R • C A Spherical Mirror: section of a sphere. light ray • principal axis C light ray principal axis C = Center of curvature In front (positive) of concave mirror, Behind (negative) convex mirror. Physics 104, Spring 2010

  7. Concave Mirror R Principal Axis Focus f=R/2 Rays parallel to principal axisand near the principal axis (“paraxial rays”) all pass through the “Focus” F. The distance from F to the center of the mirror is called the “Focal Length”, f. Physics 104, Spring 2010

  8. ConvexMirror R Principal Axis Focus f=-R/2 Rays parallel to principal axisand near the principal axis (“paraxial rays”) appear to originate from the “Focus” F. The distance from F to the center of the mirror is called the “Focal Length”, f. Physics 104, Spring 2010

  9. Question How far from the paper to be ignited should the mirror be held? farther than the focal length closer than the focal length at the focal length What kind of spherical mirror, concave or convex, can be used to start a fire? Concave Convex Flat Physics 104, Spring 2010

  10. Concave Mirror f F Principal Axis Rays traveling from focus hit mirror and are reflected parallel to Principal Axis. Rays traveling parallel to Principal Axis hit mirror and are reflected through focus. Physics 104, Spring 2010

  11. Concave Mirror Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. O #1 #2 Image is: Real (light rays actually cross) Inverted (Arrow points opposite direction) Diminished (smaller than object) #3 f c I **All other rays from object tip which hit the mirror will reflect through image tip Physics 104, Spring 2010

  12. PREFLIGHT Which ray is NOT correct? 12 3 Ray through center reflects back on self. 1) R f 2) 3) Physics 104, Spring 2010

  13. PREFLIGHT • Compared to the original arrow the image is? • Larger • Smaller • The same size p.a. R f Physics 104, Spring 2010

  14. Mirror Equation p= distance object is from mirror (+ in front - behind) q= distance image is from mirror (+ in front - behind) f = focal length of mirror (+ in front - behind) p Mirror Equation: O f c An arrow is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location. I q q = 3 cm in front of mirror Physics 104, Spring 2010

  15. SIGNS • p: positive is side light comes from (before hitting mirror or lens) • q: positive is side light goes to (after hitting mirror or lens) positive is REAL image negative Virtual • f: positive is side light goes to (after hitting mirror or lens) positive is converging negative diverging +p +p +f +f +q +q Lens Mirror Physics 104, Spring 2010

  16. Convex Mirror Question Where should you place an object in front of a convex mirror to produce a real image? • Object close to mirror • Object far from mirror • Either close or far • You can’t Mirror Equation: Physics 104, Spring 2010

  17. Convex Mirror Question Where should you place an object in front of a convex mirror to produce a real image? • Object close to mirror • Object far from mirror • Either close or far • You can’t Mirror Equation: • Convex mirror: f < 0 • Object in front of mirror: p> 0 q is negative! p is positive • Real image means q > 0 f is negative Physics 104, Spring 2010

  18. Preflight The image produced by a convex mirror of a real object is: • Always Real • Always Virtual • Sometimes Real, Sometimes Virtual Convex mirror: f < 0 Real Object means in front of mirror: p> 0 Mirror Equation: q is <0 Physics 104, Spring 2010

  19. Question Where in front of a concave mirror should you place an object so that the image is virtual? • Object close to mirror • Object far from mirror • Either close or far • Image can never be virtual Physics 104, Spring 2010

  20. Question Where in front of a concave mirror should you place an object so that the image is virtual? Mirror Equation: • Object close to mirror • Object far from mirror • Either close or far • Image can never be virtual • Concave mirror: f > 0 • Object in front of mirror: p> 0 • Virtual image means behind mirror: q< 0 • When p < f then q < 0 virtual image. Physics 104, Spring 2010

  21. Magnification= h’/h Draw ray which strikes mirror at principle axis p Angle of incidence O h p q I h’ Angle of reflection q Mpositive if upright Mnegative if inverted Physics 104, Spring 2010

  22. Question Where in front of a concave mirror should you place an object so that the image is upright? • close to mirror • far from mirror • both close and far • neither close nor far Need q < 0 So p < f Physics 104, Spring 2010

  23. Question A 4 inch arrow pointing down is placed in front of a mirror that creates an image with a magnification of –2. • What is the size of the image? • 2 inches • 4 inches • 8 inches 4 inches Magnitude gives us size. • What direction will the image arrow point? • Up2) Down (-) sign tells us it’s inverted from object Physics 104, Spring 2010

  24. Convex Mirror Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. #1 O #3 I #2 c f Image is: Virtual Upright Diminished Physics 104, Spring 2010

  25. Mirror Equation p= distance object is from mirror (+ in front - behind) q = distance image is from mirror (+ in front - behind) f = focal length of mirror (+ in front - behind) p Mirror Equation: O I f An arrow is placed 6 cm in front of a convex mirror with focal length f=-3 cm. Determine the image location. q q = -2 cm Behind mirror Physics 104, Spring 2010

  26. Mirror Summary • Angle of incidence = Angle of Reflection • Principal Rays • Parallel to P.A.: Through focus • Through focus: Parallel to P.A. • Through center: Back on self • |f | = R/2 • 1/f = 1/p + 1/q • Signs: light is always “in front” of mirror = + • M = -q / p Physics 104, Spring 2010

  27. PREFLIGHT • An organic chemistry student accidentally drops a glass marble into a silver nitrate mirroring solution, making the outside of the marble reflective. What kind of mirror is the marble now? • Concave • Convex • Flat Physics 104, Spring 2010

  28. Mirror Focal Lengths A concave mirror has a positive focal length f > 0 A convex mirror has a negative focal length f < 0 What is the focal length of a flat mirror? 1) f =02) f = ∞ The flatter the mirror, the larger the radius of curvature, (e.g. the earth is round, but looks flat) Physics 104, Spring 2010

  29. Preflight The image produced by a concave mirror of a real object is: • Always Real • Always Virtual • Sometimes Real, Sometimes Virtual Concave mirror: f > 0 Real Object means in front of mirror: p> 0 Mirror Equation: q can be negative or positive! Physics 104, Spring 2010

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