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 C = Center of curvature principal axis In front of concave mirror, behind convex mirror. Student: What determines the focal length of a concave mirror? f = R/2 C Convex mirror PHY132 Lecture 18, Pg2
Real-life Examples PHY132 Lecture 18, Pg3
Concave Mirror Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. Image is: Real (light rays actually cross) Inverted (Arrow points opposite direction O #3 c #1 #2 f Diminished (smaller than object) I * Any other ray from object tip which hits mirror will reflect through image tip ** Ray-tracing is reversible! PHY132 Lecture 18, Pg4
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, Pg5
Clicker Question 0: True or False. It is possible to see a virtual image. (a) (b) True False PHY132 Lecture 18, Pg6
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 With a real image you could place a screen at d i and see the image on the screen
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, Pg8
Signs(Mirrors) Object distance Positive: in front of mirror Negative: behind mirror Focal length Positive: Concave mirror Negative: Convex Mirror Image distance Positive: in front of mirror Negative: behind mirror Image size Positive: upright (same as object) Negative: inverted
Magnification= h i /h o Consider ray which strikes mirror at P.A. d o h o Angle of incidence O d o h i d i I Angle of reflection d i m positive if upright m negative if inverted PHY132 Lecture 18, Pg10 26
Student questions honestly i just did not get any of the pre class quiz questions pls help - a truly confused physics student that just wants chocolate How do we know if something is refracting light or reflecting light? Do some materials just naturally reflect, and others refract? How does minimum focus distance work for camera lenses? For example, if you're too close to the lens it can't get in focus. Confused about how to real image vs virtual vs object, also confused that concave can have both real and virtual If you had a hollow sphere where the inside is a mirror, and shone a laser into the sphere from a small hole, would the light's focal point be at the centre of the sphere? PHY132 Lecture 18, Pg11
(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 Clicker Question 2 & 3 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 Student: why does an image appear smaller on the back PHY132 Lecture 18, Pg12 of the spoon
Concave mirror d o >2f, image is - Real - Inverted - diminished PHY132 Lecture 18, Pg13
Concave Mirror Demo c f d o =2f, image is - Real - Inverted - Same size
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 Mirror Equation: B. Object far from mirror C. Either close or far D. Never Concave mirror: f > 0 Object in front of mirror: d o > 0 Virtual image means behind mirror: d i < 0 When d o < f then d i < 0 virtual image.
Clicker Question 5: 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
Cosmetic Mirror d o <f, image is - Virtual - Upright - magnified PHY132 Lecture 18, Pg17
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, Pg18
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, Pg19
Clicker 6: 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 Mirror Equation: Convex mirror: f < 0 Object in front of mirror: d o > 0 Real image means d i > 0 d i is negative! Are the images produced by a concave mirror always real, and a convex mirror always virtual? f is negative d o is positive
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, Pg21
Convex mirror Image is always: - Virtual - Upright - Diminished PHY132 Lecture 18, Pg22
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?
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
Concave mirror Mirror Summary d 0 <f: virtual, magnified, upright image f<d 0 <2f: real, magnified, inverted image d 0 >2f: real, diminished, inverted image Convex mirror Virtual, diminished, upright image PHY132 Lecture 18, Pg25