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Chapter 23. Ray 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. In this chapter you will learn: • Use the ray model of light • • • • Calculate angles of reflection and refraction Understand the color and dispersion Use ray tracing to analyze lens and mirror systems Use refraction theory to calculate the properties of lens systerm Reading assignment • • • • • • • • The Ray Model of Light Reflection Refraction Image Formation by Refraction Color and Dispersion Thin Lenses: Ray Tracing Thin Lenses: Refraction Theory Image Formation with Spherical Mirrors Stop to think 23.1 Stop to think 23.2 Stop to think 23.3 Stop to think 23.4 Stop to think 23.5 Stop to think 23.6 Example 23.2 Example 23.4 Example 23.9 Example 23.11 Example 23.17 page 703 page706 page 711 page 720 page 724 page 731 page 705 page 709 page 719 page 722 page 730 Propagation of Light – Ray (Geometric) Optics Main assumption: light travels in a straight-line path in a uniform medium and changes its direction when it meets the surface of a different medium or if the optical properties of the medium are nonuniform The rays (directions of propagation) are straight lines perpendicular to the wave fronts The above assumption is valid only when the size of the barrier (or the size of the media) is much larger than the wavelength of light d 4 Stop to think 23.1 A long, thin light bulb illuminates a vertical aperture. Which pattern of light do you see on a viewing screen behind the aperture? C Reading quiz 1 A virtual image is A virtual image is A.the cause of optical illusions. B.a point from which rays appear to diverge. C.an image that only seems to exist. D.the image that is left in space after you remove a viewing screen. A.the cause of optical illusions. B.a point from which rays appear to diverge. C.an image that only seems to exist. D.the image that is left in space after you remove a viewing screen. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Reading quiz 2 The focal length of a converging lens is The focal length of a converging lens is A.the distance at which an image is formed. B.the distance at which an object must be placed to form an image. C.the distance at which parallel light rays are focused. D.the distance from the front surface to the back surface. A.the distance at which an image is formed. B.the distance at which an object must be placed to form an image. C.the distance at which parallel light rays are focused. D.the distance from the front surface to the back surface. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Reflection The law of reflection states that 1. The incident ray and the reflected ray are in the same plane normal to the surface, and 2. The angle of reflection equals the angle of incidence: θr = θi Reflection of Light Specular reflection (reflection from a smooth surface) – example: mirrors Diffuse reflection (reflection from a rough surface) 10 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. Two plane mirrors form a right angle. How many images of the ball can you see in the mirrors? A. 1 B. 2 C. 3 D. 4 C Refraction Snell’s law states that if a ray refracts between medium 1 and medium 2, having indices of refraction n1 an n2, the ray angles θ1 and θ2 in the two media are related by Notice that Snell’s law does not mention which is the incident angle and which is the refracted angle. Refraction – Snell’s Law • The incident ray, the refracted ray, and the normal all lie on the same plane • The angle of refraction is related to the angle of incidence as sin 2 v2 sin 1 v1 – v1 is the speed of the light in the first medium and v2 is its speed in the second Since v1 sin 2 v2 c / n2 n1 c c and v2 , we get , or n2 sin 2 n1 sin 1 n1 n2 sin 1 v1 c / n1 n2 Snell’s Law index of refraction 18 Color Dispersion Different colors are associated with light of different wavelengths. The longest wavelengths are perceived as red light and the shortest as violet light. Table 23.2 is a brief summary of the visible spectrum of light. The slight variation of index of refraction with wavelength is known as dispersion. Shown is the dispersion curves of two common glasses. Notice that n is larger when the wavelength is shorter, thus violet light refracts more than red light. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Refraction in a Prism Since all the colors have different angles of deviation, white light will spread out into a spectrum Violet deviates the most Red deviates the least The remaining colors are in between 21 1 1 ' when sin 1 n= sin 2 min , sin( 2 2' min 2 sin 2 ) 2 min , 1 1 ' 2 2 2 EXAMPLE 23.4 Measuring the index of refraction EXAMPLE 23.4 Measuring the index of refraction QUESTION: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 23.4 Measuring the index of refraction Total Internal Reflection Total Internal Reflection: Application Fiber Optics • Plastic or glass rods are used to “pipe” light from one place to another Total Internal Reflection ( incidence cr ) • Applications include: – medical use of fiber optic cables for diagnosis and correction of medical problems – Telecommunications 28 A triangular glass prism with an apex angle of Ф=60o has an index of refraction n=1.5. What is the smallest angle of incidence for which a light ray can emerge from the other side? Thin Lenses: Ray Tracing Thin Lenses: Ray Tracing Thin Lenses: Ray Tracing Lateral Magnification The image can be either larger or smaller than the object, depending on the location and focal length of the lens. The lateral magnification m is defined as 1. A positive value of m indicates that the image is upright relative to the object. A negative value of m indicates that the image is inverted relative to the object. 2. The absolute value of m gives the size ratio of the image and object: h'/h = |m| . Important Concepts Applications