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SPH3UW: OPTICS I Introduction to Mirrors Light incident on an object Absorption Everything true for wavelengths << object size Reflection (bounces)**

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Presentation on theme: "SPH3UW: OPTICS I Introduction to Mirrors Light incident on an object Absorption Everything true for wavelengths << object size Reflection (bounces)**"— Presentation transcript:

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2 SPH3UW: OPTICS I Introduction to Mirrors

3 Light incident on an object Absorption Everything true for wavelengths << object size Reflection (bounces)** See it Mirrors Refraction (bends) Lenses Often some of each

4 Reflection i r Angle of incidence = Angle of reflection i = r i = r (Angles between light beam and normal)

5 Object Location Light rays from sun bounce off object and go in all directions Some of the rays hit your eyes Some of the rays hit your eyes We know objects location by the direction the light rays come from. Color: some light is absorbed by object before bouncing off.

6 Reflection from a Plane Mirror The angle of incidence equals the angle of reflection. This assumes the surface is perfectly smooth.

7 Diffuse Reflection When the surface is rough, the surface at any point makes some angle with respect to the horizontal. The angle of incidence still equals the angle of reflection.

8 Plane Mirrors In the left hand picture with a rough surface, you can place your eye anywhere and you will see some reflected rays. On the right hand side, you eye has to be in the correct position to see the reflected light. This is called specular reflection.

9 Plane Mirrors A plane mirror provides the opportunity to fool you by making your eye and brain perceive an image.

10 Plane Mirrors The image appears to be the same distance behind the mirror as the object is in front of the mirror.

11 Plane Mirrors The image is called a virtual image because if you placed a piece of paper at the image location, you wouldnt see any light.

12 Plane Mirror All you see is what reaches your eyes. You think objects location is where rays appears to come from. r i Object Image All rays originating from peak will appear to come from same point behind mirror!

13 How to Draw the Image in a Plane Mirror (3) Where the extended lines appear to intersect (a distance d behind mirror) is the image location. d d (1) Draw first ray perpendicular to mirror i =0 0 = r (2) Draw second or third ray at angle. i = r Light rays dont really converge there, so its a Virtual Image r i Virtual: No light actually gets here. r i

14 How Big a Mirror? 0.80 m

15 Why do ambulances have AMBULANCE written backwards? Question

16 Solution So you can read it in your rear-view mirror!

17 Question Can you see Fidos tail in mirror? mirror (You)(Fido)

18 Solution Can you see Fidos tail in mirror? mirror No! (You) (Fido) You need light rays from the tail to bounce off mirror and reach your eye!

19 ACT: Plane Mirrors 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: (1)closer to the mirror. (2)further from the mirror. (3)to another mirror.

20 Changing distance doesnt change what you see of yourself ACT: Plane Mirrors 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: (1)closer to the mirror. (2)further from the mirror. (3)to another mirror.

21 Two Mirrors How many images of money will you see (not including the actual money)?

22 1 Two Mirrors How many images of money will you see (not including the actual money)? 2 3

23 R Curved mirrors A Spherical Mirror: section of a sphere. C = Center of Curvature In front of concave mirror Behind convex mirror. C = Center of Curvature In front of concave mirror Behind convex mirror. principal axis light ray Concave mirror R C Convex mirror principal axis light ray R C

24 Understanding 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 this? (1) concave (2) convex (3) flat

25 Concave Mirror Principal Axis Focus Rays parallel to principal axis and near the principal axis (paraxial rays) all reflect so they pass through theFocus (F). R f=R/2 The distance from F to the center of the mirror is called the Focal Length (f). Rays are bent towards the principal axis.

26 What kind of spherical mirror can be used to start a fire? concave convex 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 Understanding

27 Concave Mirror Principal Axis FF Rays traveling through focus before hitting mirror are reflected parallel to Principal Axis. Rays traveling parallel to Principal Axis before hitting mirror are reflected through focus

28 Convex Mirror Principal AxisFocus Rays parallel to principal axis and near the principal axis (paraxial rays) all reflect so they appear to originate from the Focus (F). R f=-R/2 The distance from F to the center of the mirror is called the Focal Length (f). Rays are bent away from the principal axis.

29 Concave Mirror –Drawing image f c 1) Parallel to principal axis reflects through f. #1 3) Through center. #3 Image is (in this case): Real or Imaginary Inverted or Upright Reduced or Enlarged **Every other ray from object tip which hits mirror will reflect through image tip. You need at least two of the above techniques to draw image 2) Through f, reflects parallel to principal axis. #2 4) At the vertex V #4 When object is on the outside of the centre of curvature Technique

30 The image is real The image is inverted The image is smaller than the object Concave Mirror –Drawing image When object is on the outside of the centre of curvature

31 Concave Mirror-Drawing images f c 1) Parallel to principal axis reflects through f. #1 Image is (in this case): Real or Imaginary Inverted or Upright Reduced or Enlarged or Same Size **Every other ray from object tip which hits mirror will reflect through image tip 2) Through f, reflects parallel to principal axis. #2 3) At the vertex When object is at the centre of curvature Technique #3 V

32 Concave Mirror-Drawing images f c 1) Parallel to principal axis reflects through f. #1 Image is (in this case): Real or Imaginary Inverted or Upright Reduced or Enlarged **Every other ray from object tip which hits mirror will reflect through image tip 2) Through f, reflects parallel to principal axis. #2 When object is between the centre of curvature and the focus Technique 3) At the vertex #3 V

33 Concave Mirror Principal Rays f c 1) Parallel to principal axis reflects through f. #1 Image is (in this case): Real or Imaginary Inverted or Upright Reduced or Enlarged **Every other ray from object tip which hits mirror will reflect through image tip 2) Through f, reflects parallel to principal axis. #2 When object is between the focus and the Vertex Technique #3 V 3) At the vertex

34 Concave Mirror Principal Rays When object is between the focus and the Vertex The image is virtual The image is upright The image is larger than the object

35 R f 1) 2) 3) p.a. Understanding Which ray is NOT correct? Ray through centre should reflect back on self.

36 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 =0(2) f = Mirror Focal Lengths The flatter the mirror, the larger the radius of curvature, (e.g. the earth is round, but looks flat)

37 Concave Mirror Image Location Yep, no image

38 O I Mirror Equation c dodo didi d o = distance object is from mirror: Positive: object is _______ of mirror Negative: object is _______ mirror d i = distance image is from mirror: Positive: _______ image is __________ of mirror Negative: _______ image is__________ mirror f = focal length mirror: Positive: _________ mirror Negative: _________ mirror f In Front Behind In Front Behind In front behind Inverted upright Inverted upright invertedIn front upright behind Concave Convex Concave Convex concave convex

39 Understanding The image produced by a concave mirror of a real object is: 1)Always Real 2)Always Virtual 3)Sometimes Real, Sometimes Virtual In a concave mirror the focal length, f, is >0 Real Object means in front of mirror: d o > 0 Therefore d i can be positive or negative Mirror Equation

40 Practice: Concave Mirror Where in front of a concave mirror should you place an object so that the image is virtual? Mirror Equation: 1)Close to mirror 2)Far from mirror 3)Either close or far 4)Not Possible When d o < f then d i <0 : virtual image. Virtual image means behind mirror: d i < 0 Object in front of mirror: d o > 0 In a concave mirror the focal length, f, is > 0

41 O I Magnification Equation dodo dodo hoho Angle of incidence didi hihi Angle of reflection didi h o = height of object: Positive:_______________ h i = height of image: Positive: ______________ Negative: _____________ m = magnification: Positive / Negative: same as for h i < 1: image is _______________ > 1: image is ________________ Always upright inverted reduced enlarged

42 Practice Solving Equations A candle is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location. (in front of mirror) Real Image! C f p.a. Compared to the candle, the image will be: Larger Smaller Same Size Note: image is 3 cm in front of mirror, therefore 1 cm to the left of the focus

43 What is the size of the image? 1)2 inches 2)4 inches 3)8 inches What direction will the image arrow point? 1)Up2) Down (-) sign tells us its inverted from object Magnitude gives us size. 4 inches Practice: Magnification A 4 inch arrow pointing down is placed in front of a mirror that creates an image with a magnification of –2.

44 O Convex Mirror Rays c 1) Parallel to principal axis reflects through f. 3) Through f, reflects parallel to principal axis. #3 I 2) Through center. #2 Image is: Virtual (light rays dont really cross) Upright (same direction as object) Reduced (smaller than object) (always true for convex mirrors!): f #1 Technique

45 Convex Mirror Rays The image is virtual The image is upright The image is smaller than the object

46 Convex Mirror Images Unlike Concave Mirrors, convex mirrors always produce images which share these characteristics. The location of the object does not affect the characteristics of the image. As such, the characteristics of the images formed by convex mirrors are easily predictable The diagrams below shows that in each case: the image is located behind the convex mirror a virtual image an upright image reduced in size (i.e., smaller than the object)

47 Overview Reflection: Refraction: Absorption Flat Mirror: image equidistant behind Spherical Mirrors: Concave or Convex Flat Lens: Window Spherical Lenses: Concave or Convex Today Last Time Next time i r 1 2 n2n2 n1n1 i = r n 1 sin( 1 )= n 2 sin( 2 )

48 Solving Problems A candle is placed 6 cm in front of a convex mirror with focal length f=-3 cm. Determine the image location. Determine the magnification of the candle. If the candle is 9 cm tall, how tall does the image candle appear to be? Image is Upright! d i = - 2 cm (behind mirror) Virtual Image!

49 Problem Where should you place an object in front of a convex mirror to produce a real image? Mirror Equation: 1)Object close to mirror 2)Object far from mirror 3)Either close or far 4)You cant d i is negative! f is negative d o is positive Real image means d i > 0 Convex mirror: f < 0 Object in front of mirror: d o > 0

50 Problem A concave mirror has a radius of curvature of 24.0 cm. An object 2.5 cm high is placed 40.0 cm in front of the mirror. a)At What distance from the mirror will the image be formed? b)What is the height of the image? C f

51 Problem A concave mirror has a radius of curvature of 24.0 cm. An object 2.5 cm high is placed 40.0 cm in front of the mirror. a)At What distance from the mirror will the image be formed? b)What is the height of the image? C f The image is 17 cm in front of the mirror

52 Problem A concave mirror has a radius of curvature of 24.0 cm. An object 2.5 cm high is placed 40.0 cm in front of the mirror. a)At What distance from the mirror will the image be formed? b)What is the height of the image? C f The height of the inverted image is 1.1 cm

53 Problem C f A convex mirror has a radius of curvature of 80.0 cm. An object 1.7 m high is placed 4.5 m in front of the mirror. a)At What distance from the mirror will the image be formed? b)What is the height of the image?

54 Problem C f A convex mirror has a radius of curvature of 80.0 cm. An object 1.7 m high is placed 4.5 m in front of the mirror. a)At What distance from the mirror will the image be formed? b)What is the height of the image? Therefore the image is 0.37 m behind the mirror

55 Problem C f A convex mirror has a radius of curvature of 80.0 cm. An object 1.7 m high is placed 4.5 m in front of the mirror. a)At What distance from the mirror will the image be formed? b)What is the height of the image?

56 Mirror Summary Angle of incidence = Angle of Reflection Principal Rays Parallel to P.A.: Reflects through focus Through focus: Reflects parallel to P.A. Through center: Reflects back on self |f| = R/2


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