Homework #1. Reading: Chaps. 14, 20, 21, 23. Suggested exercises: 23.6, 23.7, 23.8, 23.10, 23.12, 23.13, 23.14, 23.15

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1 Homework #1 Reading: Chaps. 14, 20, 21, 23 Suggested exercises: 23.6, 23.7, 23.8, 23.10, 23.12, 23.13, 23.14, Problems: 23.39, 23.40, 23.41, 23.42, 23.44, 23.45, 23.47, 23.48, 23.49, 23.53, (due: Fri., Aug. 28) A Brief History of Light Willebrod Snell Dutch discovered law of refraction (Snell's law) A Dutch mathematician who is best known for the law of refraction, a basis of modern geometric optics; but this only become known after his death when Huygens published it. Sir Isaac Newton English developed theories of gravitation and mechanics, and invented differential calculus 1

2 A Brief History of Light Robert Hooke English discovered Hooke's law of elasticity made contributions to many different fields including mathematics, optics, mechanics, architecture and astronomy. He had a famous quarrel with Newton. Christiaan Huygens Dutch proposed a simple geometrical wave theory of light, now known as ``Huygen's principle''; pioneered use of the pendulum in clocks A Brief History of Light Thomas Young British studied light and color; known for his double-slit experiment that demonstrated the wave nature of light did work in surface tension, elasticity, and gave one of the earliest scientific definitions of energy. His studies of the Rosetta stone contributed greatly to the deciphering of the ancient Egyptian hieroglyphic writing. Augustin-Jean Fresnel French studied transverse nature of light waves, and he was one of the founders of the wave theory of light. 2

3 A Brief History of Light James Clerk Maxwell Scottish propounded the theory of electromagnetism; developed the kinetic theory of gases Lecture #1 Chapter 23. Ray Optics (Geometric Optics) Our everyday experience that light travels in straight lines is the basis of the ray model of light. Ray optics apply to a variety of situations, including mirrors, lenses, and shiny spoons. Chapter Goal: To understand and apply the ray model of light. 3

4 Chapter 23. Ray Optics Topics: The Ray Model of Light Principles governing Ray model: Reflection Refraction Image Formation by Refraction Color and Dispersion Thin Lenses: Ray Tracing Thin Lenses: Refraction Theory Image Formation with Spherical Mirrors Chapter 23. Basic Content and Examples 4

5 Propagation In a homogenous medium, a light ray propagates along a straight line Shadow Point light source Object Propagation 5

6 Ray Model of Light Light rays travel in straight lines Light ray can cross A light ray travels forever unless it interacts with matter (why?) An object is a source of light rays (selfluminous objects or reflective objects) The eye sees by focusing a diverging bundle of rays Object Point source Parallel bundle (beam) Aperture Definitions Questions regarding shadows: point source, parallel source, no shadow? 6

7 Reflection Light interacts with an opaque object. Specular reflection Diffuse reflection Reflection The law of reflection states that 1. The incident ray and the reflected ray are in the same plane normal to the surface (incident plane) 2. The angle of reflection equals the angle of incidence: θ r = θ i How about reflection from a curved surface? 7

8 The Plane Mirror s s The Plane Mirror Consider P, a source of rays which reflect from a mirror. The reflected rays appear to emanate from P', the same distance behind the mirror as P is in front of the mirror. That is, s' = s. Under what condition can you see the image of the object? Virtual image 8

9 Refraction Light interacts with transparent object. Refraction Light interacts with transparent object. 9

10 Refraction Snell s law states that if a ray refracts between medium 1 and medium 2, having indices of refraction n 1 an n 2, the ray angles θ 1 and θ 2 in the two media are related by (1621 Willebrord Snellius, Dutch mathematician) Notice that Snell s law does not mention which is the incident angle and which is the refracted angle. Index of refraction Speed of light in vacuum n Speed of light in a medium c v In vacuum, Speed of Light 8 c m/ s In medium, v c Thus, n 1 10

11 Can n be negative? What would happen if n becomes negative? Metamaterials!!! Electromagnetic cloaking devices, super lenses, filters, sub wavelength waveguides and antennas e_index_about.htm 11

12 Snell s law Refraction n1 sin n sin If n 1 < n 2, then θ 1 > θ 2 n 1 1 n 2 2 Snell s law n Refraction 1 sin 1 n2 sin 2 If n 1 > n 2, then θ 1 < θ 2 n n 2 12

13 Snell s law Refraction n1 sin n sin If θ 1 = 0, then θ 2 = 0, regardless the values of n 1 and n 2 n 1 n 2 Total Internal Reflection 13

14 Total Internal Reflection Snell s law n1 sin n sin n 2 If n 2 < n 1, then θ 2 > θ 1 n sin n 1 2 sin 2 1 When n2 sin 1 sin c n 1 90 o 2 When n sin 1 n 2 1 n 1 Total internal reflection occurs Total Internal Reflection Optical fibers A laser bouncing down a perspex rod illustrating the total internal reflection of light in a multimode optical fiber Charles Kuen Kao The Nobel Prize in Physics 2009 Watch this video: 14

15 Total Internal Reflection Invisible Glass Why does the glass rod vanish in another liquid? 15

16 Color Different colors are associated with light of different wavelengths. The longest wavelengths are perceived as red light and the shortest as violet light. Color Questions 16

17 Dispersion The slight variation of index of refraction with wavelength is known as dispersion. Notice that n is larger when the wavelength is shorter, thus violet light refracts more than red light. Dispersion 17

18 Dispersion If n 1 < n 2, Dispersion 18

19 Dispersion If n 1 > n 2, Rainbow 19

20 Three Laws of Geometric Optics 1. Propagation in homogenous medium 2. Law of reflection 3. Law of refraction Ray Model Example 1.1 An albatross glides at a constant 15m/s horizontally above level ground, moving in a vertical plane that contains the Sun. It glides toward a solid wall of height h = 2.0 m, which it will just barely clear. At that time of day, the angle of the Sun relative to the ground is = 30 o. At what speed does the shadow of the albatross move (a) across the level ground and the (b) up the wall? Sunray h 20

21 Reflection In-Class Activity #1 The following figure shows light reflecting from two perpendicular reflecting surfaces A and B. Find the angle between the incoming ray i and the outgoing ray r. i A B r r Reflection In-Class Activity #2 The following figure shows the multiple reflections of a light ray along a glass corridor where the walls are either parallel or perpendicular to one another. If the angle of incident at point a is 30 o, what are the angles of reflection of the light at point b, c, d, e, and f? 21

22 Example 1.2 A basketball player with a height of 191cm wants to see his entire height in a full-length mirror mounted on a wall. What is the least length the mirror must have? Example 1.3 In the figure you look into a system of two vertical parallel mirrors A and B separated by distance d. A toy monkey is hanged at point O, a distance 0.2d from mirror A. Each mirror produces a first (least deep) image of the monkey. Then each mirror produces a second image with the object being the first image in the opposite mirror. Then each mirror produces a third image with the object being the second image in the opposite mirror, and so on you might see hundreds of monkey images. How deep behind mirror A are the first, second and third images in mirror A? 22

23 In-Class Activity #3 The following figure shows rays of monochromic light passing through three materials a, b, and c. Rank the materials according to their indexes of refraction, greatest first. Tactics: Analyzing refraction 23

24 EXAMPLE 23.4 Measuring the index of refraction QUESTION: EXAMPLE 23.4 Measuring the index of refraction 24

25 EXAMPLE 23.4 Measuring the index of refraction EXAMPLE 23.4 Measuring the index of refraction 25

26 EXAMPLE 23.4 Measuring the index of refraction EXAMPLE 23.4 Measuring the index of refraction 26

27 Example 1.4 In the figure, a 2.00-m-long vertical pole extends from the bottom of a swimming pool to a point 50.0 cm above the water. Sunlight is incident at 55.0 o above the horizon. What is the length of the shadow of the pole on the level bottom of the pool? Example 1.5 The following figure shows a triangular prism of glass in air; an incident ray enters the glass perpendicular to one face and is totally reflected at the far glass air interface as indicated. If 1 is 45 o, what can you say about the index of refraction n of the glass? 27

28 Example 1.6 A submerged swimmer is looking directly upward through the air-water interface in a pool. Over what range of angles do rays reach the swimmer s eyes from light sources external to the water? Assume that the light is monochromatic and that the index of refraction of water is Similar to example 23.5 Optional Course Materials 28

29 Reversibility of Rays When the propagation direction of a light ray is reversed, it will follow the same (old) path. 1 θ i n θ r 2 θ 2 29