Lecture 17 Mirrors and Thin Lens Equation

LECTURE 17 MIRRORS AND THIN LENS EQUATION

18.6 Image formation with Spherical mirrors are everywhere! spherical mirrors Concave mirrors Convex mirrors 18.7 The thin-lens equation Sign conventions for lenses and mirrors 18.6 Image formation with spherical mirrors

! Spherical mirrors (concave mirrors and convex mirrors) can be used to form images. Quiz: 18.6-1

! When an object is placed very far away from the mirror, how far away from the mirror is the image formed in terms of its focal length, !? Enter the number without !. Quiz: 18.6-1 answer / Demo

! 1

! Since the object is very far away from the mirror, the rays from that object is parallel to each other.

! If an object is placed at a focal point, the rays emerge parallel to each other.

! One Candle Searchlight ! Demonstration of object placed at the focal plane of the mirror. 18.6 Concave mirrors

! The special rays for a concave mirror: 18.6 Concave mirrors

! For the ray trace, incoming rays are drawn as if they are reflect off the mirror plane, not off the curved surface of the mirror.

! The image is real if rays converge at the image point. 18.6 Convex mirrors

! The special rays for a convex mirror: 18.6 Convex mirrors

! Diverging rays appear to diverge from the virtual image. 18.7 The thin-lens equation & Sign conventions for lenses and mirrors

! The thin-lens equation (for thin ! Focal length, &: lenses and mirrors): ! + for a converging lens or a concave mirror ! − for a diverging lens or a convex mirror 1 1 1 ! Magnification, (: + = ! + for upright image " "$ & ! − for inverted image $ ! Image distance, " : ! + for a real images ! − for a virtual images

! Object distance, ": ! + always Quiz: 18.7-1

! When you place your face near a spherical concave mirror, inside its focal point, which of the following is/are correct? Choose all that apply. ! The image of your face is A. Diminished. B. Enlarged. C. Upright. D. Inverted. E. Real. F. Virtual. Quiz: 18.7-1 answer

! Enlarged, Upright, Virtual. Your face image here. ! This is how a make-up / shaving mirror works. Your face here. ! ! ! ! + = , where 0 < ) < *. " "$ & + "& ! ) = < 0, so the image is virtual. ",& "$ ! - = − > 0, so the image is upright. " 01 $ " 021 & ! - = = = > 1, so the image is " " ",& enlarged. Quiz: 18.7-2

! An object is placed at a location ! < # < 2!, where !%is the focal length of a concave mirror. Which of the following is/are correct about the image formed? Choose all that apply. A. Real B. Virtual C. Upright D. Inverted E. Enlarged F. Diminished Quiz: 18.7-2 answer / Demo

! Real, inverted, and enlarged ! ! ! ! + = , where ' < ) < 2'. " "$ & + "& ! ) = > 0, so the image is real. ",& "$ ! / = − < 0, so the image is inverted. " & ! / = > 1, so the image is enlarged. ",&

! Large concave mirror with strawberries and candles Example shown for ) = 604cm, and ' = 404cm. ! Demonstration of object placed outside of the focal point, forming a real inverted image. ! ) = 2', so the magnification is / = & − & = & = 1. ",& 2&,& & Quiz: 18.7-3

! A convex mirror has a magnitude of its focal length of 12 cm. What is the image distance (with an appropriate sign) for an object located near the axis at a distance of 12 cm from the mirror in cm? Quiz: 18.7-3 answer

! −6#cm#

! & = −12#cm (“−” for a convex mirror)

! * = 12#cm + + + ! + = , ,. / 0 ,/ +2#34 1+2#34 ! * = = = −6#cm ,1/ +2#34 1 1+2#34 Quiz: 18.7-4

! A convex mirror has a magnitude of its focal length of 12 cm. An object is located near the axis at distance of 12 cm from the mirror. Which of the following descriptions is correct about the image formed? Choose all that apply. A. Real B. Virtual C. Upright D. Inverted E. Enlarged F. Diminished Quiz: 18.7-4 answer

! virtual, upright, and diminished. ! ! = 12%cm

! ( = −12%cm * ! ! = −6%cm * ! ! = −6%cm < 0, so the image is virtual. /0 12%34 ! . = − = − > 0, so the image is upright. / 56%34 12%34 ! . = − = 0.5 < 1, so the image is diminished. 56%34 ! All images of a convex mirror are always virtual, upright, and diminished.

! Convex mirrors are used as passenger-side rearview mirrors and in stores to keep an eye on customers. Because the image is smaller, you can see much more of it. Demo: lens equation applied for a lens

! Image Formation ! Demonstration of a double convex lens forming an inverted and diminished or enlarged image. ! ! ! " + = " "$ & ! ! ! " + = , where ) is the distance between the light source and the screen. " '(" & '± ',(-'& " * = . Quiz: 18.7-5

! A lens creates an image as shown. In this situation, the object distance is

A. larger than the focal length. B. equal to the focal length. C. smaller than focal length. Quiz: 18.7-5

! The object distance is larger than the focal length. " ! The refracted rays converge at the real image: ! > 0.

! This is a converging lens: % > 0.

! ! > 0 always. & & & ! + = ' ') + & & ! must be smaller than . ' +

! ! > % Quiz: 18.7-6 (Knight P18.27, modified)

! A dentist uses a curved mirror to view the back side of teeth on the upper jaw. Suppose she wants an erect image with a magnification of 2.0 when the mirror is 1.2 cm from a tooth. (Treat this problem as though the object and image lie along a straight line.)

! What is its focal length in cm? Quiz: 18.7-6 (Knight P18.27, modified) answer

! What is its focal length in cm? $% ! The magnification: ! = − $ ' ! & = −!& ( ( ( ! The thin-lens equation: + = $ $% * $,$% $, ./$ ./$ . 0.2 (.034 ! + = = = = = 2.4,cm $-$% $- ./$ (./ (. 0.2

! Follow-up: Is it a convex or concave mirror? Quiz: 18.7-6 (Knight P18.27, modified) answer

! What is its focal length in cm? $% ! The magnification: ! = − $ ' ! & = −!& ( ( ( ! The thin-lens equation: + = $ $% * $,$% $, ./$ ./$ . 0.2 (.034 ! + = = = = = 2.4,cm $-$% $- ./$ (./ (. 0.2

! Follow-up: Is it a convex or concave mirror?

! Concave since the focal length is a positive value.