3/10/2019. Models of Light. Waves and wave fronts. Wave fronts and rays

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1 Models of Light The wave model: Under many circumstances, light exhibits the same behavior as material waves. The study of light as a wave is called wave optics. The ray model: The properties of prisms, mirrors, and lenses are best understood in terms of light rays. The ray model is the basis of ray optics. The photon model: In the quantum world, light behaves like neither a wave nor a particle. Instead, light consists of photons that have both wave-like and particle-like properties. This is the quantum theory of light Pearson Education, Inc. Slide 32-1 Waves and wave fronts A wave front is the locus of all adjacent points at which the phase of a wave is the same. Spherical wave fronts of sound spread out uniformly in all directions from a point source. Electromagnetic waves in vacuum also spread out as shown here. Wave fronts and rays It s often convenient to represent a light wave by rays rather than by wave fronts. A ray is an imaginary line along the direction of travel of the wave. When waves travel in a homogeneous isotropic material, the rays are always straight lines normal to the wave fronts. 1

2 Wave fronts and rays Far away from a source, where the radii of the spheres have become very large, a section of a spherical surface can be considered as a plane, and we have a plane wave. Light from Objects Objects can be either self-luminous, such as the sun and lightbulbs, or they can be reflective. Most objects are reflective Pearson Education, Inc. Slide 34-5 Ray Diagrams Rays originate from every point on an object and travel outward in all directions, but a diagram trying to show all these rays would be messy and confusing. To simplify the picture, we use a ray diagram showing only a few rays Pearson Education, Inc. Slide

3 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: r = i 2017 Pearson Education, Inc. Slide 34-7 Example 1 A dressing mirror on a closet door is 1.50 m tall. The bottom is 0.50 m above the floor. A bare lightbulb hangs 1.00 m from the closet door, 2.50 m above the floor. How long is the streak of reflected light across the floor? 2017 Pearson Education, Inc. Slide 34-8 Diffuse and specular reflection Our primary concern in this chapter will be with specular reflection from a very smooth surface such as highly polished glass or metal (a). Scattered reflection from a rough surface is called diffuse reflection (b). The vast majority of objects in your environment are visible to you because they reflect light in a diffuse manner. 3

4 The Plane Mirror Consider P, a source of rays that 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 2017 Pearson Education, Inc. Slide The Plane Mirror 2017 Pearson Education, Inc. Slide QuickCheck You are looking at the image of a pencil in a mirror. What do you see in the mirror if the top half of the mirror is covered with a piece of dark paper? A. The full image of the pencil B. The top half only of the pencil C. The bottom half only of the pencil D. No pencil, only the paper 2017 Pearson Education, Inc. Slide

5 Example 2 If your height is h, what is the shortest mirror on the wall in which you can see your full image? Where must the top of the mirror be hung? 2017 Pearson Education, Inc. Slide In-class Activity #1 A light ray leaves point A in the figure, reflects from the mirror, and reaches point B. How far below the top edge does the ray strike the mirror? 2017 Pearson Education, Inc. Slide Refraction Two things happen when a light ray is incident on a smooth boundary between two transparent materials: 1. Part of the light reflects from the boundary, obeying the law of reflection. 2. Part of the light continues into the second medium. The transmission of light from one medium to another, but with a change in direction, is called refraction Pearson Education, Inc. Slide

6 Index of refraction The index of refraction of an optical material (also called the refractive index), denoted by n, is defined as: For the case shown here, material b has a larger index of refraction than material a (n b > n a ) and the angle θ b is smaller than θ a. Reflection and refraction: Case 1 of 3 When a ray passes from one material into another material having a larger index of refraction and hence a slower wave speed, the angle θ b with the normal is smaller in the second material than the angle θ a in the first. Reflection and refraction: Case 2 of 3 When a ray passes from one material into another material having a smaller index of refraction and hence a faster wave speed, the angle θ b with the normal is larger in the second material than the angle θ a in the first. 6

7 Reflection and refraction: Case 3 of 3 In the case of normal incidence, the transmitted ray is not bent at all. In this case θ a = 0 and sin θ a = 0, so θ b is also equal to zero; the transmitted ray is also normal to the interface. θ r is also equal to zero, so the reflected ray travels back along the same path as the incident ray. The law of refraction This result is also called Snell s law, after the Dutch scientist Willebrord Snell ( ). Why does the ruler appear to be bent? The law of refraction explains why a partially submerged straight ruler appears bent. Light rays coming from below the surface change in direction at the air water interface, so the rays appear to be coming from a position above their actual point of origin. 7

8 Why does the ruler appear to be bent? QuickCheck Light passes from vacuum (index of refraction n = 1) into water (n = 1.333). If the incident angle is an acute angle A. the refracted angle is greater than the incident angle. B. the refracted angle is equal to the incident angle. C. the refracted angle is less than the incident angle. D. two of A, B, and C are possible, depending on the specific value of Pearson Education, Inc. QuickCheck Light passes from a medium of index of refraction n a into a second medium of index of refraction n b. The angles of incidence and refraction are respectively. If n a < n b, A. and the light speeds up as it enters the second medium. B. and the light slows down as it enters the second medium. C. and the light speeds up as it enters the second medium. D. and the light slows down as it enters the second medium Pearson Education, Inc. 8

9 QuickCheck A laser beam passing from medium 1 to medium 2 is refracted as shown. Which is true? A. n 1 < n 2 B. n 1 > n 2 C. There s not enough information to compare n 1 and n Pearson Education, Inc. Slide Indices of Refraction 2017 Pearson Education, Inc. Slide QuickCheck When light passes from vacuum (index of refraction n = 1) into water (n = 1.333), A. the wavelength increases and the frequency is unchanged. B. the wavelength decreases and the frequency is unchanged. C. the wavelength is unchanged and the frequency increases. D. the wavelength is unchanged and the frequency decreases. 9

10 Index of refraction and the wave aspects of light The frequency f of a wave does not change when passing from one material to another. In any material, v = λf ; since f is the same in any material as in vacuum and v is always less than the wave speed c in vacuum, λ is also correspondingly reduced. When a wave passes from one material into a second material the waves get squeezed (the wavelength gets shorter) if the wave speed decreases and get stretched (the wavelength gets longer) if the wave speed increases. Refraction The figure shows a wave crossing the boundary between two media, where we re assuming n 2 > n 1. Because the wavelengths differ on opposite sides of the boundary, the wave fronts can stay lined up only if the waves in the two media are traveling in different directions Pearson Education, Inc. Slide Example 3 In the figure, material a is water and material b is glass with index of refraction The incident ray makes an angle of 60.0º with normal; find the directions of the reflected and refracted rays Pearson Education, Inc. Slide

11 Example 4 What is the prism s index of refraction? 2017 Pearson Education, Inc. Slide Example 5 The wavelength of the red light from a helium-neon laser is 633 nm in air but 474 nm in the aqueous humor inside your eyeball. Calculate the index of refraction of the aqueous humor and the speed and frequency of the light in it Pearson Education, Inc. Slide Example 6 Two mirrors are perpendicular to each other as seen in the figure. A ray traveling in the xy-plane is reflected from one mirror at P, then the other at Q. What is the ray s final direction relative to its original direction? 2017 Pearson Education, Inc. Slide

12 In-class Activity #2 Find the index of refraction for material X. Also, determine the angle the light makes with the normal in the air Pearson Education, Inc. Slide