PHY 112: Light, Color and Vision. Lecture 11. Prof. Clark McGrew Physics D 134. Review for Exam. Lecture 11 PHY 112 Lecture 1

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1 PHY 112: Light, Color and Vision Lecture 11 Prof. Clark McGrew Physics D 134 Review for Exam Lecture 11 PHY 112 Lecture 1

2 From Last Time Lenses Ray tracing a Convex Lens Announcements The midterm is Thursday During class on Thursday, March 4 Multiple choice (bring a #2 pencil) Closed book, no notes (I'll bring scratch paper) You will need a calculator Should do sines and cosines Lecture 11 PHY 112 Lecture 2

3 Light is a Electromagnetic Wave Properties of Light Velocity: 300,000,000 m/s (i.e. 3 x 10 8 m/s) in vacuum Constant speed in vacuum But can slow down in materials Light moves Described by Energy Momentum Wavelength, frequency, period, polarization, amplitude, intensity Lecture 11 PHY 112 Lecture 3

4 Symbols for Light Symbols to represent ideas: Wavelength: λ Velocity: v This is the Greek letter Lambda Because l is easily confused with 1 and I The velocity of light (in vacuum) gets a special symbol: c Period: T Frequency: f The book gets clever and uses the Greek letter Nu (ν) Lecture 11 PHY 112 Lecture 4

5 Important Equation Relate the velocity of light to it's frequency and wavelength v= f Lecture 11 PHY 112 Lecture 5

6 The Electromagnetic Spectrum Visible Light ~400 nm to 700 nm Lecture 11 PHY 112 Lecture 6

7 Reflection and Transmission Waves change velocity at a boundary The frequency is the same on both sides of the boundary Vocabulary: That means the wavelength changes (v( = fλ) Reflected: : Part of the energy reverses direction Transmitted: : Part of the energy crosses the boundary Only if the new material is also transparent For metal, wave is reflected, but not transmitted Lecture 4 PHY 112 Lecture 7

8 Relating Wave Properties to Perception Light is describe by Wavelength, Intensity We perceive Color: Related to wavelength Brightness: Related to intensity These are related, but are not the same thing For instance, our perception of brightness depends on both the wavelength and intensity Lecture 11 PHY 112 Lecture 8

9 Light Rays Give the direction of light Rays are straight Only change direction when they hit something (i.e. scatter) Light Rays are an approximation Useful, but not quite accurate We can use light rays when When sizes and distances are much greater than the wavelength Lecture 11 PHY 112 Lecture 9

10 When Do Rays Work As long as stuff is a lot bigger than the wave length Red is 650 nm Stuff bigger than nm That is about a 1/15 th of a millimeter Blue is 475 nm Stuff bigger than nm How big is that That is about 1/20 th of a millimeter A hair is about 1/10 th of a millimeter thick A piece of paper is about 1/10 th of a millimeter thick Lecture 11 PHY 112 Lecture 10

11 Light Wave Fronts Specify the position of the wave crests Tell us the direction, and phase of a wave Wave fronts have to be continuous, but can bend at a surface (e.g. refraction) Lecture 11 PHY 112 Lecture 11

12 Rays and Wave fronts Wave fronts and rays are perpendicular Lecture 11 PHY 112 Lecture 12

13 Ray Tracing Screen Light Source Light Rays Tells us where the light will hit Lecture 11 PHY 112 Lecture 13

14 Principal Rays Principal Rays We only need to draw the principal rays which are the ones where something changes For lenses and mirrors we concentrated on the principal rays Lecture 11 PHY 112 Lecture 14

15 Names for Shadows Penumbra Umbra Penumbra Lecture 11 PHY 112 Lecture 15

16 How Does a Mirror Work Glass (called a substrate) Back surface mirror Reflector (called a coating) Usually made of a metal Lecture 11 PHY 112 Lecture 16

17 Law of Reflections The normal is perpendicular The angle of incidence... Is equal to the angle of reflection Lecture 11 PHY 112 Lecture 17

18 Specular and Diffuse Reflection Specular Reflection Diffuse Reflection Lecture 11 PHY 112 Lecture 18

19 Natural Mirrors Specular Reflection Object Virtual Image Lecture 11 PHY 112 Lecture 19

20 Sun Glitter (Diffuse Reflection) The projector screen is also diffuse reflection Lecture 11 PHY 112 Lecture 20

21 Index of Refraction Light Speeds Speed of light in vacuum is a universal constant, c Speed of light in a material is a property of the material (e.g. c glass ) Index of refraction n material = speed of light in vacuum speed of light in material Lecture 11 PHY 112 Lecture 21

22 Index of Refraction Material Index of Refraction Vacuum 1 Air Just more than 1 Water 1.33 Glass 1.3 to 1.5 speed of light in material= speed of light in vacuum n material Lecture 11 PHY 112 Lecture 22

23 Example Light is traveling in a material with an index of refraction, n = 1.2. What is the velocity of the light in the material? speed of light in vacuum speed of light in material= n material The speed of light in vacuum is 3 x 10 8 m/s, so speed in material= m/ s 1.2 = m/s Lecture 11 PHY 112 Lecture 23

24 Refraction Normal Incident Ray θ I n I n R θ R Refracted Ray Lecture 11 PHY 112 Lecture 24

25 Snell's Law n incident sin incident =n refracted sin refracted sin refracted = n incident n refracted sin incident sin incident = n refracted n incident sin refracted Lecture 11 PHY 112 Lecture 25

26 Example Light travels from air into water (n = 1.33) with a 30 degree angle of incidence. What is the angle of refraction? sin refracted = n incident n refracted sin incident The index of refraction for air is n = 1, so sin refracted = 1 sin 30= refracted =arcsin 0.376=22 degrees Lecture 11 PHY 112 Lecture 26

27 SOH-CAH-TOA Sine is Opposite over Hypotenuse sin θ = O/H Cosine is Adjacent over Hypotenuse cos θ = A/H Tangent is Opposite over Adjacent tan θ = O/A H O θ Lecture 11 PHY 112 Lecture 27 A

28 What does Snell's Law Tell Us? Light going from a small index of refraction (air) to a large index of refraction (glass) is bent toward the normal. Light going from a large index of refraction (glass) to a small index of refraction (air) is bent away from the normal. Lecture 11 PHY 112 Lecture 28

29 Describing a Spherical Mirror Radius (twice Focal Length) Optical Axis Focal Point Focal Length Center If center is in front of mirror (concave), the focal length is positive If center is in back of mirror (convex), the focal length is negative Lecture 11 PHY 112 Lecture 29

30 Example A spherical mirror has a 1 meter radius of curvature. What is it's focal length? f = R/2 so f = 50 cm Lecture 11 PHY 112 Lecture 30

31 General Spherical Mirror Ray Tracing Rules 3 2 Focal Point 1 Start on one of the yellow lines, end up on one of the red lines. And vice-versa... 4 A ray on line 1 goes to line 2 A ray on line 2 goes to line 1 A ray on line 3 goes to line 4 A ray on line 4 goes to line 3 Lecture 11 PHY 112 Lecture 31

32 Convex Mirror Ray Tracing Rules All incident rays parallel to the axis appear to come from the focal point. All incident rays that (when extended) pass through the focal point are reflected back parallel to the axis. A virtual image is formed where the previous two rays cross. Lecture 11 PHY 112 Lecture 32

33 A Convex Mirror Image Distance Object Distance The image is behind the mirror, so the image distance is negative! Optical Axis Object Virtual Image Virtual image is closer to mirror than the object. Lecture 11 PHY 112 Lecture 33

34 Concave Mirror Ray Tracing Rules Object closer than focal point Draw a line from the focal point passing through the tip of the object to the mirror. Draw a ray along this line from the object to the mirror. It will be reflected parallel to the axis Draw a ray from the tip of the object parallel to the axis. It will be reflected through the focal point. Extend the rays behind the mirror. There will be a virtual image where they cross. Lecture 11 PHY 112 Lecture 34

35 A Concave Mirror (object close to mirror) Object Distance Image Distance Light doesn't actually come from virtual image... Virtual Image Object The image is behind the mirror, so the image distance is negative! Image is further from mirror than object Lecture 11 PHY 112 Lecture 35

36 Ray Tracing a Concave Mirror Object further than focal point A ray going parallel to the axis are reflected through the focal point. A ray going through the focal point is reflected parallel to the axis A real image is formed where the rays cross. Lecture 11 PHY 112 Lecture 36

37 A Concave Mirror (object far from mirror) Object Distance Object Real Image Object and image are further from focal point Image Distance Lecture 11 PHY 112 Lecture 37

38 Mirror Equations We can also rearrange to get the magnification The Mirror Equation:1 / f = 1 / X O + 1 / X I The magnification: m = S I /S O = - X I / X O Notice the magnification is negative for a concave mirror with a real image! Lecture 11 PHY 112 Lecture 38

39 Example A mirror has a focal length of 50 cm. If the object distance is 80 cm, what is the image distance? so 1 / f = 1 / X O + 1 / X I X = 1/(1/f 1/X ) I o 1/(1/(50 cm) 1/(80 cm)) = 133 cm The magnification is m = - X i /X o = This is a real image. Lecture 11 PHY 112 Lecture 39

40 Ray Tracing Rules For a Lens Focal Point 1 A ray on line 1 goes to line 2 Start on one of the yellow lines, end up on one of the red lines. And vice-versa... Lecture 11 PHY 112 Lecture A ray on line 2 goes to line 1 A ray on line 3 goes to line 4 A ray on line 4 goes to line 340

41 Convex Lens Ray Tracing Rules Object closer than focal point Draw a line from the focal point passing through the tip of the object to the lens. Draw a ray along this line from the object to the lens. It will be refracted parallel to the axis Draw a ray from the tip of the object to the lens parallel to the axis. It will be refracted through the focal point. Extend the rays back to the other side of the mirror There will be a virtual image where they cross. Lecture 11 PHY 112 Lecture 41

42 Ray Trace a Convex Lens Object closer than focus Image Distance Focal Length Object Distance Focal Point Focal Point Optical Axis Virtual Image Object Lecture 11 PHY 112 Lecture 42

43 Good Luck on the Midterm Lecture 11 PHY 112 Lecture 43

44 The End Lecture 11 PHY 112 Lecture 44