Physics 132: Lecture Fundamentals of Physics II Mirrors Agenda for Today Concave Convex Mirror equation
Curved Mirrors A Spherical Mirror: section of a sphere. R light ray C Concave mirror principal axis light ray principal axis C = Center of curvature In front of concave mirror, behind convex mirror. C Convex mirror PHY132 Lecture 18, Pg2
Concave Mirror Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal 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 PHY132 Lecture 18, Pg3
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: O d o An arrow is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location. c I d i f d i = 3 cm in front of mirror PHY132 Lecture 18, Pg4
Clicker Question 0: True or False. It is possible to see a virtual image. (a) (b) True False PHY132 Lecture 18, Pg5
Virtual vs. Real image Virtual image: image where light rays do not actually emanate from/through image point Real image: image where light rays do actually emanate from/through image point
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. PHY132 Lecture 18, Pg7
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
Magnification= h i /h o Draw ray which strikes mirror at P.A. d o h o Angle of incidence O d o h i d i Angle of reflection I d i m positive if upright m negative if inverted PHY132 Lecture 18, Pg9 26
When you look at your reflection in the bowl of a spoon, it is upside down. (1) Why? a. it s a concave mirror forming real image. b. it s a concave mirror forming virtual image. c. it s magic Clicker Question 2 & 3 (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 PHY132 Lecture 18, Pg10
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
Cosmetic Mirror PHY132 Lecture 18, Pg12
Convex Mirror Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal 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 PHY132 Lecture 18, Pg13
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: O d 0 I An arrow is placed 6 cm in front of a convex mirror with focal length f=-3 cm. Determine the image location. d i f d i = -2 cm Behind mirror PHY132 Lecture 18, Pg14
Clicker 5: Where should you place an object in front of a convex mirror to produce a real image? A. Object close to mirror B. Object far from mirror C. Either close or far D. You can t
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. PHY132 Lecture 18, Pg16
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. PHY132 Lecture 18, Pg17
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/d o + 1/d i Behind mirror is negative, in front is positive m = -d i / d o
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?