Physics 132: Lecture Fundamentals of Physics

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1 Physics 132: Lecture Fundamentals of Physics II Agenda for Today Mirrors Concave Convex e Mirror equation Physics 201: Lecture 1, Pg 1

2 Curved mirrors A Spherical Mirror: section of a sphere. R light ray C Concave mirror principal p axis light ray principal axis C = Center of curvature In front of concave mirror, behind convex mirror. C Convex mirror Physics 201: Lecture 1, Pg 2

3 Concave Mirror Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal p axis. 3) Through center. O #1 Image is: Real (light rays actually cross) Inverted (Arrow points opposite direction Diminished (smaller than object) #3 c #2 I f **Any other ray from object tip which hits mirror will reflect through image tip Physics 201: Lecture 1, Pg 3

4 Mirror Equation f = focal length of mirror (+ in front - behind) d o = distance object is from mirror (+ in front - behind) d i = distance image is from mirror (+ in front - behind) Mirror Equation: d o d i f o i O c An arrow is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location. d o I d i f 1 6 cm 1 d i 1 2 cm d i = 3 cm in front of mirror Physics 201: Lecture 1, Pg 4

5 Clicker Question 1: A concave mirror brings the sun's rays to a focus in front of the mirror. Suppose the mirror is submerged in a swimming pool but still pointed up at the sun. Will the sun's rays be focused nearer to, farther from, or at the same distance from the mirror? (a) (b) (c) Nearer to the mirror The same distance from the mirror Farther from the mirror. Physics 201: Lecture 1, Pg 5

6 Object Signs(Mirrors) Positive: in front of mirror Negative: behind mirror (oops! using a concave as a convex or vice versa) Focal length Positive: Concave mirror Negative: Convex Mirror Image Positive: in front of mirror Negative: behind mirror Generally, call the object s side of the mirror the + direction, and then all the other signs follow Physics 201: Lecture 1, Pg 6

7 PCQ: Clicker Question 2 When you look at your reflection in the bowl of a spoon, it is upside down. (1) Why? (2) Where is your head relative to the focal length of the spoon? a. closer to the spoon than the focal length b. further away from the spoon than the focal length c. at the focal length Physics 201: Lecture 1, Pg 7

8 Magnification= h i /h o Draw ray which h strikes mirror at PA P.A. d o h o Angle of incidence O h i d i d o I tan( ) h d o o m hi di hi d h d o i o Angle of reflection d i m positive if upright m negative if inverted Physics 201: Lecture 1, Pg 8 26

9 Clicker Question 3: A negative magnification for a mirror means that A. the image is inverted, and the mirror is concave. B. the image is inverted, and the mirror is convex. C. the image is inverted, and the mirror may be concave or convex. D. the image is upright, and the mirror may be concave or convex. E. the image is upright, and the mirror is convex. Physics 201: Lecture 1, Pg 9

10 Clicker 4: Where in front of a concave mirror should you place an object so that the image is virtual? A. Object close to mirror B. Object far from mirror C. Either close or far D. Never Physics 201: Lecture 1, Pg 10

11 Convex Mirror Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal p axis. 3) Through center. O #1 #2 #3 I Image is: Virtual (light rays don t really cross) Upright (same direction as object) Diminished (smaller than object) f c **For a real object, image is always virtual, upright and diminished Physics 201: Lecture 1, Pg 11

12 Mirror Equation d 0 = distance object is from mirror (+ in front - behind) d i = distance image is from mirror (+ in front - behind) f = focal length of mirror (+ in front - behind) Mirror Equation: d o d i f o i An arrow is placed 6 cm in front of a convex mirror with focal length f=-3 cm. Determine the image location. O d 0 d i f I cm d i 1 3 cm d i = -2 cm i Behind mirror Physics 201: Lecture 1, Pg 12

13 Clicker 5: Where should you place an object in front of a convex mirror to produce a real image? 1) Object close to mirror 2) Object far from mirror 3) Either close or far 4) You can t Physics 201: Lecture 1, Pg 13

14 Clicker Question 6: You see an upright, magnified image of your face when you look into magnifying cosmetic mirror. The image is located A. In front of the mirror s surface. B. On the mirror s surface. C. Behind the mirror s surface. D. Only in your mind because it s a virtual image. Physics 201: Lecture 1, Pg 14

15 Clicker Question 7: The rear-view mirrors on the passenger side of many cars have a warning statement: "OBJECTS IN MIRROR ARE CLOSER THAN THEY APPEAR." This means that the nature of the mirror must be A. concave. B. plane. C. convex. D. transparent. Physics 201: Lecture 1, Pg 15

16 Mirror Summary Angle of incidence id = 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/d o + 1/d i Behind mirror is negative, in front is positive m = -d i / d o Physics 201: Lecture 1, Pg 16 39

17 Example: An object's image in a 24 cm -focal-length concave mirror is upright and magnified by a factor of 3.0. How far is the object from the mirror? Physics 201: Lecture 1, Pg 17

18 Converging Lens All rays parallel to principal axis pass through focal point F n 1 n 1 P.A. n 2 >n 1 F Double Convex Physics 201: Lecture 1, Pg 18

19 Converging Lens Principal Rays Object F F P.A. Image 1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays through F emerge parallel to principal axis. Image is real, inverted and enlarged Assumptions: monochromatic light incident on a thin lens. rays are all near the principal axis. Physics 201: Lecture 1, Pg 19

20 Ray tracing for a converging lens This could be used in a camera This could be used as a projector This is a magnifying glass Physics 201: Lecture 1, Pg 20

21 Clicker Question 7: 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? A) f =0 B) f = Physics 201: Lecture 1, Pg 21

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