HW Chapter 20 Q 2,3,4,5,6,10,13 P 1,2,3. Chapter 20. Classic and Modern Optics. Dr. Armen Kocharian

Transcription

1 HW Chapter 20 Q 2,3,4,5,6,10,13 P 1,2,3 Chapter 20 Classic and Modern Optics Dr. Armen Kocharian

2 Electromagnetic waves and matter: A Brief History of Light 1000 AD It was proposed that light consisted of tiny particles Newton Used this particle model to explain reflection and refraction Huygens 1678 Explained many properties of light by proposing light was wave-like

3 A Brief History of Light, cont Young 1801 Strong support for wave theory by showing interference for particles (electrons) Maxwell 1865 Electromagnetic waves travel at the speed of light

4 A Brief History of Light, final Planck EM radiation is quantized Implies particles Explained light spectrum emitted by hot objects Einstein Particle nature of light Explained the photoelectric effect

5 The Particle Nature of Light Particles of light are called photons Each photon has a particular energy E = h ƒ h is Planck s constant h = 6.63 x J s Encompasses both natures of light Interacts like a particle Has a given frequency like a wave

6 Dual Nature of Light Experiments can be devised that will display either the wave nature or the particle nature of light In some experiments light acts as a wave and in others it acts as a particle Nature prevents testing both qualities at the same time

7 Geometric Optics Using a Ray Approximation Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media The ray (beam) approximation is used to represent beams of light A ray of light is an imaginary line drawn along the direction of travel of the light beams

8 Ray Approximation A wave front is a surface passing through points of a wave that have the same phase and amplitude The rays, corresponding to the direction of the wave motion, are perpendicular to the wave fronts

9 Reflection of Light A ray of light, the incident ray, travels in a medium When it encounters a boundary with a second medium, part of the incident ray is reflected back into the first medium This means it is directed backward into the first medium

10 Specular Reflection Specular reflection is reflection from a smooth surface The reflected rays are parallel to each other All reflection in this text is assumed to be specular

11 Diffuse Reflection Diffuse reflection is reflection from a rough surface The reflected rays travel in a variety of directions Diffuse reflection makes the dry road easy to see at night

12 Law of Reflection The normal is a line perpendicular to the surface It is at the point where the incident ray strikes the surface The incident ray makes an angle of θ 1 with the normal The reflected ray makes an angle of θ 1 with the normal

13 Law of Reflection, cont The angle of reflection is equal to the angle of incidence θ 1 = θ 1

14 Refraction of Light When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium The ray that enters the second medium is bent at the boundary This bending of the ray is called refraction

15 Refraction of Light, cont The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane The angle of refraction, θ 2, depends on the properties of the medium

16 Bending of Light Rays Ray bend at the boundary of materials with various refraction indexes

17 Following the Reflected and Refracted Rays Ray 1 is the incident ray Ray 2 is the reflected ray Ray 3 is refracted into the lucite Ray 4 is internally reflected in the lucite Ray 5 is refracted as it enters the air from the lucite

18 More About Refraction The angle of refraction depends upon the material and the angle of incidence sinθ1 v2 constant sinθ = v = 2 1 The path of the light through the refracting surface is reversible

19 Refraction Details, 1 Light may refract into a material where its speed is lower The angle of refraction is less than the angle of incidence The ray bends toward the normal

20 Refraction Details, 2 Light may refract into a material where its speed is higher The angle of refraction is greater than the angle of incidence The ray bends away from the normal

21 The Index of Refraction When light passes from one medium to another, it is refracted because the speed of light is different in the two media The index of refraction, n, of a medium can be defined n speed of light in a vacuum = = speed of light in a medium c v

22 Index of Refraction, cont For a vacuum, n = 1 For other media, n > 1 n is a unitless ratio

23 Frequency Between Media As light travels from one medium to another, its frequency does not change Both the wave speed and the wavelength do change The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same

24 Index of Refraction Extended The frequency stays the same as the wave travels from one medium to the other v = ƒ λ The ratio of the indices of refraction of the two media can be expressed as various ratios c λ1 v1 n1 n2 λ = c 2 v = = 2 n1 n 2

25 Some Indices of Refraction

26 Snell s Law of Refraction n 1 sin θ 1 = n 2 sin θ 2 θ 1 is the angle of incidence 30.0 in this diagram θ 2 is the angle of refraction

27 Flat Refracting Surface The image formed by a flat refracting surface is on the same side of the surface as the object The image is virtual The image forms between the object and the surface The rays bend away from the normal since n 1 > n 2

28 Light bending There are many interesting results of refraction in the atmosphere Apparent depth

29 Atmospheric Refraction There are many interesting results of refraction in the atmosphere Sunsets Mirages

30 Atmospheric Refraction and Sunsets Light rays from the sun are bent as they pass into the atmosphere It is a gradual bend because the light passes through layers of the atmosphere Each layer has a slightly different index of refraction The Sun is seen to be above the horizon even after it has fallen below it

31 Atmospheric Refraction and Mirages A mirage can be observed when the air above the ground is warmer than the air at higher elevations The rays in path B are directed toward the ground and then bent by refraction The observer sees both an upright and an inverted image

32 Atmospheric Mirages A mirage is observed when the air above the ground is warmer than the air at higher elevations The rays in path B are directed toward the ground and then bent by refraction

33 Dispersion The index of refraction in anything except a vacuum depends on the wavelength of the light This dependence of n on λ is called dispersion Snell s Law indicates that the angle of refraction made when light enters a material depends on the wavelength of the light

34 Variation of Index of Refraction with Wavelength The index of refraction for a material usually decreases with increasing wavelength Violet light refracts more than red light when passing from air into a material

35 Refraction in a Prism The amount the ray is bent away from its original direction is called the angle of deviation, δ Since all the colors have different angles of deviation, they will spread out into a spectrum Violet deviates the most Red deviates the least

36 Prism Spectrometer A prism spectrometer uses a prism to cause the wavelengths to separate The instrument is commonly used to study wavelengths emitted by a light source

37 Using Spectra to Identify Gases All hot, low pressure gases emit their own characteristic spectra The particular wavelengths emitted by a gas serve as fingerprints of that gas Some uses of spectral analysis Identification of molecules Identification of elements in distant stars Identification of minerals

38 The Rainbow A ray of light strikes a drop of water in the atmosphere It undergoes both reflection and refraction First refraction at the front of the drop Violet light will deviate the most Red light will deviate the least

39 The Rainbow, 2 At the back surface the light is reflected It is refracted again as it returns to the front surface and moves into the air The rays leave the drop at various angles The angle between the white light and the violet ray is 40 The angle between the white light and the red ray is 42

40 Dispersion Newton demonstration of the dispersion of the light Phenomenon explains how the water droplets can disperse the light

41 Observing the Rainbow If a raindrop high in the sky is observed, the red ray is seen A drop lower in the sky would direct violet light to the observer The other colors of the spectra lie in between the red and the violet

42 Physics and world of color The colors of objects are produced by combining of the three primary additive colors The color printing combines dots of three primary subtractive colors: cyan, yellow and magenta

43 Polarized scattered light The sky appears blue because short waves (blue light) are scattered (σ=1/λ 4 ) much more strongly off the air molecules The light, when we look away from the sun, is blue

44 Light scattering The light from sun is traveled through atmosphere is scattered (σ=1/λ 4 ) so only the less scattered one (red color) reaches the observer at sunset.

45 Christian Huygens Best known for contributions to fields of optics and dynamics Deduced the laws of reflection and refraction Explained double refraction

46 Huygen s Principle Huygen assumed that light is a form of wave motion rather than a stream of particles Huygen s Principle is a geometric construction for determining the position of a new wave at some point based on the knowledge of the wave front that preceded it

47 Huygen s Principle, cont All points on a given wave front are taken as point sources for the production of spherical secondary waves, called wavelets, which propagate in the forward direction with speeds characteristic of waves in that medium After some time has elapsed, the new position of the wave front is the surface tangent to the wavelets

48 Huygen s Construction for a Plane Wave At t = 0, the wave front is indicated by the plane AA The points are representative sources for the wavelets After the wavelets have moved a distance cδt, a new plane BB can be drawn tangent to the wavefronts

49 Huygen s Construction for a Spherical Wave The inner arc represents part of the spherical wave The points are representative points where wavelets are propagated The new wavefront is tangent at each point to the wavelet

50 Total internal reflection An angle of incidence becomes larger than the critical value

51 Critical Angle A particular angle of incidence will result in an angle of refraction of 90 This angle of incidence is called the critical angle n2 sinθ C = for n 1 > n 2 n1

52 Critical Angle, cont For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary This ray obeys the Law of Reflection at the boundary Total internal reflection occurs only when light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction

53 Fiber Optics An application of internal reflection Plastic or glass rods are used to pipe light from one place to another Applications include medical use of fiber optic cables for diagnosis and correction of medical problems Telecommunications

54 Notation for Mirrors and Lenses The object distance is the distance from the object to the mirror or lens Denoted by p The image distance is the distance from the image to the mirror or lens Images are formed at the point where rays actually intersect or appear to originate Denoted by q The lateral magnification of the mirror or lens is the ratio of the image height to the object height Denoted by M

55 Types of Images for Mirrors and Lenses A real image is one in which light actually passes through the image point Real images can be displayed on screens A virtual image is one in which the light does not pass through the image point The light appears to diverge from that point Virtual images cannot be displayed on screens

56 More About Images To find where an image is formed, it is always necessary to follow at least two rays of light as they reflect from the mirror

57 Flat Mirror Simplest possible mirror Properties of the image can be determined by geometry One ray starts at P, follows path PQ and reflects back on itself A second ray follows path PR and reflects according to the Law of Reflection

58 Properties of the Image Formed by a Flat Mirror The image is as far behind the mirror as the object is in front q = p The image is unmagnified The image height is the same as the object height h = h and M = 1 The image is virtual The image is upright It has the same orientation as the object There is an apparent left-right reversal in the image

59 Spherical Mirrors A spherical mirror has the shape of a segment of a sphere A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curve A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve

60 Concave Mirror, Notation The mirror has a radius of curvature of R Its center of curvature is the point C Point V is the center of the spherical segment A line drawn from C to V is called the principle axis of the mirror

61 Spherical Aberration Rays are generally assumed to make small angles with the mirror When the rays make large angles, they may converge to points other than the image point This results in a blurred image This effect is called spherical aberration

62 Image Formed by a Concave Mirror Geometry can be used to determine the magnification of the image h' q M = = h p h is negative when the image is inverted with respect to the object

63 Image Formed by a Concave Mirror Geometry shows the relationship between the image and object distances = p q R This is called the mirror equation

64 Focal Length If an object is very far away, then p= and 1/p = 0 Incoming rays are essentially parallel In this special case, the image point is called the focal point The distance from the mirror to the focal point is called the focal length The focal length is ½ the radius of curvature

65 Focal Point and Focal Length, cont The focal point is dependent solely on the curvature of the mirror, not by the location of the object f = R / 2 The mirror equation can be expressed as = p q f

66 Focal Length Shown by Parallel Rays

67 Convex Mirrors A convex mirror is sometimes called a diverging mirror The rays from any point on the object diverge after reflection as though they were coming from some point behind the mirror The image is virtual because it lies behind the mirror at the point where the reflected rays appear to originate In general, the image formed by a convex mirror is upright, virtual, and smaller than the object

68 Image Formed by a Convex Mirror

69 Ray Diagrams A ray diagram can be used to determine the position and size of an image They are graphical constructions which tell the overall nature of the image They can also be used to check the parameters calculated from the mirror and magnification equations

70 Drawing A Ray Diagram To make the ray diagram, you need to know The position of the object The position of the center of curvature Three rays are drawn They all start from the same position on the object The intersection of any two of the rays at a point locates the image The third ray serves as a check of the construction

71 The Rays in a Ray Diagram Ray 1 is drawn parallel to the principle axis and is reflected back through the focal point, F Ray 2 is drawn through the focal point and is reflected parallel to the principle axis Ray 3 is drawn through the center of curvature and is reflected back on itself

72 Notes About the Rays The rays actually go in all directions from the object The three rays were chosen for their ease of construction The image point obtained by the ray diagram must agree with the value of q calculated from the mirror equation

73 Ray Diagram for Concave Mirror, p > R The object is outside the center of curvature of the mirror The image is real The image is inverted The image is smaller than the object

74 Ray Diagram for a Concave Mirror, p < f The object is between the mirror and the focal point The image is virtual The image is upright The image is larger than the object

75 Ray Diagram for a Convex Mirror The object is in front of a convex mirror The image is virtual The image is upright The image is smaller than the object

76 Notes on Images With a concave mirror, the image may be either real or virtual When the object is outside the focal point, the image is real When the object is at the focal point, the image is infinitely far away When the object is between the mirror and the focal point, the image is virtual With a convex mirror, the image is always virtual and upright As the object distance increases, the virtual image gets smaller

77 Thin Lenses A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane Lenses are commonly used to form images by refraction in optical instruments

78 Thin Lens Shapes These are examples of converging lenses They have positive focal lengths They are thickest in the middle

79 More Thin Lens Shapes These are examples of diverging lenses They have negative focal lengths They are thickest at the edges

80 Focal Length of Lenses The focal length, ƒ, is the image distance that corresponds to an infinite object distance This is the same as for mirrors A thin lens has two focal points, corresponding to parallel rays from the left and from the right A thin lens is one in which the distance between the surface of the lens and the center of the lens is negligible

81 Focal Length of a Converging Lens The parallel rays pass through the lens and converge at the focal point The parallel rays can come from the left or right of the lens

82 Focal Length of a Diverging Lens The parallel rays diverge after passing through the diverging lens The focal point is the point where the rays appear to have originated

83 Lens Equations The geometric derivation of the equations is very similar to that of mirrors h' q M = = h p = p q f

84 Lens Equations The equations can be used for both converging and diverging lenses A converging lens has a positive focal length A diverging lens has a negative focal length

85 Focal Length for a Lens The focal length of a lens is related to the curvature of its front and back surfaces and the index of refraction of the material = ( n 1) f R R 1 2 This is called the lens maker s equation

86 Ray Diagrams for Thin Lenses Ray diagrams are essential for understanding the overall image formation Three rays are drawn The first ray is drawn parallel to the first principle axis and then passes through (or appears to come from) one of the focal lengths The second ray is drawn through the center of the lens and continues in a straight line The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis There are an infinite number of rays, these are convenient

87 Ray Diagram for Converging Lens, p > f The image is real The image is inverted

88 Ray Diagram for Converging Lens, p < f The image is virtual The image is upright

89 Ray Diagram for Diverging Lens The image is virtual The image is upright

90 Combinations of Thin Lenses The image produced by the first lens is calculated as though the second lens were not present The light then approaches the second lens as if it had come from the image of the first lens The image of the first lens is treated as the object of the second lens The image formed by the second lens is the final image of the system

91 Combination of Thin Lenses, 2 If the image formed by the first lens lies on the back side of the second lens, then the image is treated at a virtual object for the second lens p will be negative The overall magnification is the product of the magnification of the separate lenses

92 Combination of Thin Lenses, example

93 Lens and Mirror Aberrations One of the basic problems is the imperfect quality of the images Largely the result of defects in shape and form Two common types of aberrations exist Spherical aberration Chromatic aberration

94 Spherical Aberration Results from the focal points of light rays far from the principle axis are different from the focal points of rays passing near the axis For a mirror, parabolic shapes can be used to correct for spherical aberration

95 Chromatic Aberration Different wavelengths of light refracted by a lens focus at different points Violet rays are refracted more than red rays The focal length for red light is greater than the focal length for violet light Chromatic aberration can be minimized by the use of a combination of converging and diverging lenses