PHYS 219 General Physics: Electricity, Light and Modern Physics
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1 PHYS 219 General Physics: Electricity, Light and Modern Physics Exam 2 is scheduled on Tuesday, March 8 10 PM In Physics 114 It will cover four Chapters 21, 22, 23, and 24. Start reviewing lecture notes, home works, and recitation problems! EXAMS: There will be two 75-minute evening exams and a two-hour final exam. The evening exams are multiple-choice and should be able to be completed within 75 minutes by a well-prepared student; note that we re giving you 120 minutes. The times and locations of the evening exams are as follows: Exam 1: Wednesday, February 8 10 PM in Physics 203 and Physics 331 Exam 2: Tuesday, March 8 10 PM in Physics 114 All exams are closed book. For the exams you will need a #2 pencil, a calculator and your student ID. You may make a single crib sheet for Exam 1 (you may write on both sides of an 8.5 x 11 sheet of paper). Bring this and a second crib sheet to Exam 2; bring both crib sheets and a third to the Final Exam. Many, but not all, formulae will be provided on the front of the Exams.
2 Chapter 24 Geometrical Optics Lecture Ray (Geometrical) Optics 24.2 Reflection from a Plane Mirror 24.3 Refraction 24.4 Reflections and Images Produced by Curved Mirrors 24.5 Lenses 24.6 How the Eye Works 24.7 Optics in the Atmosphere 24.8 Aberrations
3 Optics The study of light is called optics Some highlights in the history of optics Study of optics dates to at least third century BC Eyeglasses invented around 1300 Microscopes and telescopes invented around 1600 Applications depend on the ability of lenses and mirrors to focus light Light is an electromagnetic wave and its wave nature needs to be accounted for Introduction
4 Geometrical Optics Applies to the regime where light travels in straightline paths Effects involving wave interference are not important Describes cases in which the wavelength of the light is much smaller than the size of the objects in the light s path, object size. Wavelength of visible light is less than 1µm Describes many everyday applications Including the behavior of mirrors and lenses Introduction
5 Rays Rays indicate the path and direction of propagation of the light wave In A, the waves pass through a large opening d and, to a very good approximation, follow straight lines that pass through the opening In B, the opening is about the same size or smaller than the wavelength of the light, d, and wave optics (Chapter 25) is needed to explain the spreading of the light d d Section 24.1
6 Wave Fronts Wave front surfaces are determined by the crests and troughs of the wave They are always perpendicular to the associated rays The shape of a wave front depends on how the wave is generated and the distance from the source Section 24.1
7 Ray Tracing The method of following the individual rays as they travel from an object to some other point is called ray tracing Ray tracing involves the use of geometry The figure shows a few rays from the object There are an infinite number of actual rays The light waves associated with all the rays contribute to the image formed by your eye Section 24.1
8 Reflection from a Plane Mirror Rays may be reflected from a flat surface or a plane mirror A plane mirror is a flat surface that reflects all or nearly all the light that strikes it If the light is a plane wave, all the rays are parallel and strike a surface at many different points Section 24.2
9 Reflection from a Plane Mirror, cont. Characterize the reflection by a single ray The normal (vertical dashed line in fig. B) is perpendicular to the mirror The direction of the incoming and outgoing rays are measured relative to the normal Section 24.2
10 Law Of Reflection The incoming ray is called the incident ray The angle it makes with the normal is called the angle of incidence, θ i The outgoing ray is called the reflected ray The angle it makes with the normal is called the angle of reflection, θ r The Law of Reflection says θ i = θ r Reflection from a perfectly flat mirror is called specular reflection Section 24.2
11 Image Formation Plane Mirror/Relecting Surface An image formed by a plane mirror is shown Two representative rays are shown coming from the object There is an infinite number of rays emanating from each point on the object The rays that reflected from the mirror and reached your eyes form the image Section 24.2
12 Image Formation Characteristics of the image The distance (L) from the object to the mirror is the same as the distance from the image to the mirror The size (height) of the image, h i, is the same as the size (height) of the object, h o The image is virtual The image point is located behind the mirror The light does not actually pass through the image The same analysis can be applied to multiple mirrors Section 24.2
13 Demo - Candle Illusion
14 Refraction When a light ray strikes a transparent material, some of the light is reflected and some is refracted The reflected ray obeys the Law of Reflection The refracted ray passes into the material The incident angle is now denoted as θ 1 Section 24.3
15 Angle of Refraction The direction of the refracted ray is measured by using θ 2 (refer to fig ) The value of this angle depends on the incident angle and the speed of light in the material The speed of light in a vacuum is 3 x 10 8 m/s Fig When the light travels through a material substance, its interactions with the atoms of the material slows down the speed of the wave Section 24.3
16 Snell s Law - Refraction si The change in the speed of light from the vacuum to the material changes the direction of the wave From the geometry of the waves in the material, ct vt sin 1 sin 2 sin 1 and sin 2 L L c v c sin sin 1 2 v Section 24.3
17 Snell s Law - Refraction, cont. The ratio c/v is called the index of refraction and is denoted by n n = c / v n is unitless and n > 1 Then, sin θ 1 = n sin θ 2 This assumes the wave is incident in a vacuum A more general statement can be applied to any two materials with indices of refraction n 1 and n 2 n 1 sin θ 1 = n 2 sin θ 2 This relationship is called Snell s Law Section 24.3
18 Speeds and n s for Various Materials Section 24.3
19 Applying Snell s Law Refraction is also reversible Snell s Law applies whether light begins in the material with the larger or smaller index of refraction Possible angles of refraction are always between 0 and 90 The side with the larger index of refraction has the smaller angle n2 n1 2 1
20 Direction of Refracted Ray Light is refracted toward the normal when moving into the substance with the larger index of refraction Light is refracted away from the normal when moving into the substance with the smaller index of refraction as shown here n1 n2 1 2 Section 24.3
21 Laws of Reflection and Refraction: Summary Law of Reflection A reflected ray lies in the plane of incidence The angle of reflection is equal to the angle of incidence 1 1 Medium 1 Law of Refraction c Indenx of refraction n: n 1, v c v A refracted ray lies in the plane of incidence The angle of refraction is related to the angle of incidence by n sin n sin Snell s Law vi c / ni c 1 i where is the i f f f n n i i wavelength in vacuum Medium i=2 n n 2 1
22 Total Internal Reflection (1) The critical angle, c, at which total internal reflection n takes place is given by n Which we can rewrite as For n 2 = 1 (air) 1 sin c n sin sin sin c sin sin n air = 2 and n air =n 2 2 > 1 sin c 1 ( n n) 2 c 2 1 n1 At angles less than c, some light is reflected and some is transmitted At angles greater than c, all the light is reflected and none is transmitted
23 Total Internal Reflection (2) - Demo air > medium since n air < n medium 2 > 1
24 Optical Fibers - Demo An important application of total internal reflection is the optical fiber Optical fibers can be used to transport light from a source to a destination One type optical fiber used for digital communications consists of a glass core surrounded by cladding composed of glass with lower index of refraction than the core
25 Dispersion When light travels in a material, the speed depends on the color of the light This dependence of wave speed on color is called dispersion Since the index of refraction is slightly different for each color, the angle of refraction will be different for each color Section 24.3
26 Dispersion and Prisms Dispersion is used by a prism to separate a beam of light into its component colors There are two refractions with the prism The red and blue show the extremes of the incident beams Section 24.3
27 Curved Mirrors A curved mirror can produce an image of an object that is magnified The image can be larger or smaller than the object Magnified images are used in many applications Telescopes Car s review mirror Many others Section 24.4
28 Ray Tracing Curved Mirror A spherical mirror is one in which the surface of the mirror forms a section of a spherical shell The radius, R, of the sphere is the radius of curvature of the mirror The mirror s principal axis is the line that extends from the center of curvature, C, to the center of the mirror Section 24.4
29 Concave Spherical Mirror Properties of concave spherical mirrors Incoming rays that are close to and parallel to the principal axis reflect through a single point F F is the focal point It is located a distance ƒ, the focal length, from the mirror Rays that originate at the focal point reflect from the mirror parallel to the principal axis From reversibility of light Section 24.4
30 Image From a Concave Mirror Examples Section 24.4
31 Drawing A Ray Diagram Three rays are particularly easy to draw (1) Focal ray (2) Parallel ray (3) Central ray The focal ray From the tip of the object through the focal point Reflects parallel to the principal axis Section 24.4
32 Drawing A Ray Diagram, cont. The parallel ray From the tip of the object parallel to the principal axis Reflects through the focal point The central ray From the tip of the object through the center of curvature of the mirror Reflects back on itself The three rays intersect at the tip of the image Section 24.4
33 Properties of an Image Magnification is the ratio of the height of the image, h i, to the height of the object, h o hi m = h o By convention, the image height of an inverted image is negative Therefore, the magnification is also negative Section 24.4
34 Concave Mirror and Virtual Images Use ray tracing to find the image when the object is close to the mirror Closer than the focal point Use the same three rays The rays do not intersect at any point in the front of the mirror Section 24.4
35 Virtual Images Extrapolate the rays back behind the mirror They intersect at a single image point The rays appear to emanate from the image point behind the mirror The image is virtual because light does not actually pass through any point on the image The object and its image are on different sides of the mirror The image is upright and enlarged Section 24.4
36 Demos Candle Illusion 7A-05 Large Concave and Convex Mirrors 7A-09 Refraction 7A-21 Light Pipes 7A-24
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