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  1. 1. Nature of Waves
  2. 2. Waves <ul><li>A disturbance that travels through a material medium. </li></ul><ul><li>Carries energy. </li></ul><ul><li>Can transfer energy from one place to another without actual motion of an object or particle. </li></ul><ul><li>Some waves can travel through vacuum and do not require a material medium; </li></ul><ul><ul><ul><li>Example is Light </li></ul></ul></ul>
  3. 3. Types of Waves <ul><li>Transverse wave </li></ul><ul><ul><li>The motion of the particles at the moment the disturbance passes through is perpendicular to the propagation of the wave. </li></ul></ul><ul><ul><ul><li>Example: Light </li></ul></ul></ul>
  4. 4. continuation: Wave propagation Wave propagation Wave propagation Particle motion Particle motion Particle motion Undisturbed position Undisturbed position Undisturbed position
  5. 5. continuation: <ul><li>Longitudinal Wave </li></ul><ul><ul><li>The motion of the particles at the moment the disturbance passes through is linear to the propagation of the wave. </li></ul></ul><ul><ul><ul><li>Example: Sound </li></ul></ul></ul>
  6. 6. continuation: Wave propagation Wave propagation Wave propagation Particle motion Particle motion Particle motion Undisturbed position Undisturbed position Undisturbed position
  7. 7. Properties of Wave <ul><li>Wavelength </li></ul><ul><ul><li>The distance between two adjacent particles or points that behave in the same manner. </li></ul></ul><ul><ul><li>The unit is meter (m). </li></ul></ul><ul><ul><li>Denoted by Greek letter (“lamda” λ ) </li></ul></ul>
  8. 8. continuation: <ul><li>Period </li></ul><ul><ul><li>The time it takes for one complete wavelength to pass through a certain point. </li></ul></ul><ul><ul><li>The unit is second (s). </li></ul></ul><ul><ul><li>Denoted as capital T. </li></ul></ul>
  9. 9. continuation: <ul><li>Frequency </li></ul><ul><ul><li>The number of wave passing through a certain point per unit time. </li></ul></ul><ul><ul><li>The unit is per second or hertz (/s or s -1 ) </li></ul></ul><ul><ul><li>Reciprocal of Period (T) </li></ul></ul><ul><ul><li>Denoted by small letter f . </li></ul></ul>
  10. 10. <ul><li>Amplitude </li></ul><ul><ul><li>The maximum displacement of particle due to disturbance before returning to its undisturbed position. </li></ul></ul><ul><ul><li>The unit is meter (m). </li></ul></ul><ul><ul><li>Denoted by capital letter A. </li></ul></ul>continuation:
  11. 11. continuation: <ul><li>Speed </li></ul><ul><ul><li>Distance traveled by the disturbance per unit of time. </li></ul></ul><ul><ul><li>The Unit is meter per second (m/s). </li></ul></ul><ul><ul><li>Denoted by small letter v. </li></ul></ul>
  12. 12. continuation: λ λ A A crest trough
  13. 13. continuation: m/s v speed Meter (m) A amplitude /s, s -1 Hertz (Hz) f frequency Second (s) T Period Meter (m) λ Wavelength relation unit Symbol Quantity
  14. 14. Problem Solving: <ul><li>The frequency of a wave traveling across the string is 0.167 Hz and its wavelength is 9.00 cm. What is the period and speed of the wave? </li></ul>
  15. 15. Behavior of Wave <ul><li>Refraction </li></ul><ul><ul><li>It is the change in the wave’s direction as it crosses the boundaries between two medium </li></ul></ul>Incident Refracted Medium 1 Medium 2
  16. 16. continuation: <ul><li>Reflection </li></ul><ul><ul><li>It is the change in the wave’s direction without crossing to the adjacent medium. </li></ul></ul>Incident Reflected Medium 1 Medium 2
  17. 17. continuation: <ul><li>Interference </li></ul><ul><ul><li>It is the combination of two or more waves as they pass through the same location at the same time. </li></ul></ul>
  18. 18. continuation: <ul><li>Two kinds of Interference </li></ul><ul><ul><li>Constructive interference </li></ul></ul><ul><ul><ul><li>It happens when the waves passing through the same location are in-phase, resulting to a combined disturbance with higher amplitude. </li></ul></ul></ul>
  19. 19. continuation: <ul><ul><li>Destructive interference </li></ul></ul><ul><ul><ul><li>It happens when the waves passing through the same location are out-phase, resulting to a cancelled disturbance with lower or zero amplitude. </li></ul></ul></ul>
  20. 20. continuation: <ul><ul><li>Diffraction </li></ul></ul><ul><ul><ul><li>It is the spreading of wave after it passed through a small slit. </li></ul></ul></ul><ul><ul><ul><li>Each point at the wavefront acts as tiny source of smaller waves called wavelets. The interference among wavelets keep wave in shape. </li></ul></ul></ul><ul><ul><ul><li>However, If the slit is small enough, some of the wavelets will not be able to pass through; with no interference, the wavelets from one point will be able to propagate. </li></ul></ul></ul>wavefronts slit obstacle Diffracted wave
  21. 21. Electromagnetic Wave <ul><li>Changing electric field creates magnetic field. </li></ul><ul><li>Changing magnetic filed creates electric filed. </li></ul>
  22. 22. continuation: <ul><li>Electromagnetic waves are disturbance produced by propagating electric and magnetic fields. </li></ul><ul><li>Speed in a vacuum : </li></ul><ul><ul><li>(299,792,458 m/s or 3.00 x 10 8 m/s) </li></ul></ul><ul><ul><li>Examples: </li></ul></ul><ul><ul><ul><li>Light </li></ul></ul></ul><ul><ul><ul><li>Infrared rays </li></ul></ul></ul><ul><ul><ul><li>Ultraviolet rays </li></ul></ul></ul><ul><ul><ul><li>Radio waves </li></ul></ul></ul><ul><ul><ul><li>rays </li></ul></ul></ul>
  23. 23. continuation: <ul><li>Light is the electromagnetic wave that is visible to the eyes, with wavelengths between 4 x10 -7 m and 7 x10 -7 m and frequencies between 7 x 10 14 hertz and 4 x10 14 hertz. </li></ul>Electric field Magnetic field Direction Wavelength
  24. 24. Speed in a vacuum Where: c= speed of the electromagnetic waves (m/s) E=electric field (V/m) β = magnetic field (Weber/m 2 ) ε o = permitivity constant μ o = permeability constant
  25. 25. Problem Solving: <ul><li>At a particular time the magnetic field intensity in electromagnetic wave is 2 x10 -10 Wb/m 2 . Calculate the magnitude of the electric field intensity. </li></ul>
  26. 26. Electromagnetic Spectrum <ul><li>Assignment: </li></ul><ul><li>Computerized, Short bond paper </li></ul><ul><ul><li>Research work </li></ul></ul><ul><ul><ul><li>Gamma Rays </li></ul></ul></ul><ul><ul><ul><li>X-rays </li></ul></ul></ul><ul><ul><ul><li>Ultraviolet rays </li></ul></ul></ul><ul><ul><ul><li>Visible Light </li></ul></ul></ul><ul><ul><ul><li>Infrared </li></ul></ul></ul><ul><ul><ul><li>Radio wave </li></ul></ul></ul>
  27. 27. Wavelength and frequency <ul><li>The frequency and wavelength of electromagnetic (EM) wave are inversely proportional. </li></ul>Where: f = frequency of the wave (Hz) c = speed of the EM wave in a vacuum λ = wavelength (m)
  28. 28. Problem Solving: <ul><li>What is the range of the wavelength of the visible light? </li></ul><ul><ul><li>(see… Electromagnetic spectrum table) </li></ul></ul>
  29. 29. Visible Light
  30. 30. Visible Light <ul><li>Form of electromagnetic radiation that our eyes detect. </li></ul><ul><li>Wavelength ranging from 400 to 760 nm. </li></ul><ul><li>People are able to “see” an object ligth enters the eyes. </li></ul><ul><li>Represented as: </li></ul><ul><ul><li>Ray </li></ul></ul><ul><ul><ul><li>a thin beam of light that travel in a straight line. </li></ul></ul></ul><ul><ul><li>Wavefront </li></ul></ul><ul><ul><ul><li>It is the line (not necessarily straight) or surface connecting all the light that left a source at the same time. </li></ul></ul></ul><ul><li>Can be reflected and refracted. </li></ul>
  31. 31. Optics <ul><li>Branch of electromagnetism that deals with the nature, properties and behavior of light. </li></ul><ul><li>Two branches: </li></ul><ul><ul><li>Geometric Optics </li></ul></ul><ul><ul><ul><li>Describes light propagation in terms of rays. </li></ul></ul></ul><ul><ul><li>Physical Optics </li></ul></ul><ul><ul><ul><li>Treat light propagation as a wave phenomenon rather than a ray phenomenon. </li></ul></ul></ul>
  32. 32. Reflection of Light <ul><li>The angle of incident ( θ i ) is equal to the angle of reflection ( θ r ) </li></ul>
  33. 33. continuation: θ i θ r θ i = 0 θ r = 0 Mirror A The light is parallel to The plane of mirror. No Reflection. Mirror B Light is reflected at an angle. θ i = θ r A B Mirror C Incident and reflected Light are both perpendicular To the plane of mirror. θ i - θ r =0 C
  34. 34. Refraction of Light <ul><li>The refraction of light is governed by Snell’s Law: </li></ul>Where: θ i = angle of incident ray θ r = angle of refraction ray n i & n r = indices of refraction
  35. 35. continuation: AIR WATER Incident ray Refracted ray θ i θ r
  36. 36. continuation: <ul><li>Index of refraction (n) </li></ul><ul><ul><li>The ratio of light’s speed in a vacuum and light’s speed in that material. </li></ul></ul><ul><ul><li>Property of the material has no unit. </li></ul></ul>Where: c = 3.00 x10 8 m/s light in vacuum. v = speed of light in the medium.
  37. 37. Sample Problem: <ul><li>A light beam crosses from the vacuum to water with incident beam angle of 25.0 0 . If the index of refraction of vacuum is 1 and that of water is 1.33, what is the angle of refracted light beam? </li></ul>
  38. 38. Mirrors <ul><li>Surface that reflects so much light that they formed images. </li></ul><ul><li>Made of polish metal (silver or copper) or glass with silver colored coating. </li></ul>
  39. 39. continuation: <ul><li>Two kinds of mirror: </li></ul><ul><ul><li>Plane mirror </li></ul></ul><ul><ul><ul><li>Flat surface and the reflected parallel light rays remain parallel. </li></ul></ul></ul>Plane mirror
  40. 40. continuation: <ul><ul><li>Spherical mirror </li></ul></ul><ul><ul><ul><li>Its surface form a part of the surface of the sphere: </li></ul></ul></ul><ul><ul><ul><ul><li>Concave mirror – focuses reflected rays. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Convex mirror – scatters reflected rays. </li></ul></ul></ul></ul>Concave mirror Convex mirror Principal Axis Principal Axis
  41. 41. Parts of a mirror <ul><li>Principal axis </li></ul><ul><ul><li>An imaginary line passing through the center of the sphere and passing through the exact center of the mirror. </li></ul></ul><ul><li>Center of Curvature (C) </li></ul><ul><ul><li>The point in the center of the sphere from which the mirror was sliced. </li></ul></ul>
  42. 42. continuation: <ul><li>Vertex (V) </li></ul><ul><ul><li>The point on the mirror’s surface where the principal axis meets the mirror. </li></ul></ul><ul><ul><li>The geometric center of the mirror. </li></ul></ul><ul><li>Focal point (F) </li></ul><ul><ul><li>A point between the vertex and the center of the curvature. </li></ul></ul><ul><ul><li>In concave mirrors, this is the point where the reflected rays intersect. </li></ul></ul><ul><ul><li>In convex mirror, this is the point from where the reflected ray apparently originates. </li></ul></ul>
  43. 43. continuation: <ul><li>Radius of the curvature (R) </li></ul><ul><ul><li>Distance from the vertex to the center of the curvature. </li></ul></ul><ul><ul><li>The radius of the sphere from which the mirror was cut. </li></ul></ul><ul><li>Focal Length (f) </li></ul><ul><ul><li>The distance from the mirror to the focal point. </li></ul></ul><ul><ul><li>One-half the radius of the curvature. </li></ul></ul><ul><ul><li>For concave mirrors: </li></ul></ul><ul><ul><li>For convex mirrors: </li></ul></ul>
  44. 44. Problem Solving: <ul><li>Light from the distance is collected by a concave mirror. How far from the mirror do the light rays converge if the radius of curvature of the mirror is 200 cm.? </li></ul>
  45. 45. Mirrors Image Formation <ul><li>In Plane mirror </li></ul><ul><ul><li>In order to see the image of an object in a mirror: </li></ul></ul><ul><ul><ul><li>You must view at the image; </li></ul></ul></ul><ul><ul><ul><li>When you view at the image, light will come to your eyes along that line of sight. </li></ul></ul></ul><ul><ul><li>The image location is located at that position where observers are viewing the image of an object. It is the location behind the mirror where all the light appears to diverge from. </li></ul></ul>
  46. 46. continuation: <ul><ul><li>An image is formed because light emanates from the object in a variety of directions. </li></ul></ul><ul><ul><li>Some of this light reaches the mirror and reflects off the mirror accordingly to the law of reflection. </li></ul></ul>
  47. 47. continuation: <ul><li>In Concave mirror </li></ul><ul><ul><li>There are two types of image: </li></ul></ul><ul><ul><ul><li>Real image </li></ul></ul></ul><ul><ul><ul><ul><li>Light passes through the image’s location. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Its formed when p > f </li></ul></ul></ul></ul><ul><ul><ul><li>Virtual image </li></ul></ul></ul><ul><ul><ul><ul><li>Light does not pass through the image’s location. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Its formed when p < f </li></ul></ul></ul></ul>
  48. 48. continuation: <ul><li>In Convex mirror </li></ul><ul><ul><li>The image is always virtual. </li></ul></ul>
  49. 49. V Mirror C F For Concave Mirror Principal axis R f Object
  50. 50. V Mirror C F For Convex Mirror Principal axis f Object
  51. 51. Mirror Equation <ul><li>Where: </li></ul><ul><li>f = focal length </li></ul><ul><li>p = Object distance </li></ul><ul><ul><ul><li>Distance from the object to the mirror. </li></ul></ul></ul><ul><li>q = Image distance </li></ul><ul><ul><ul><li>Distance from the image to the mirror. </li></ul></ul></ul><ul><li>m = Magnification of the mirror </li></ul><ul><li>y = size of the object </li></ul><ul><li>y’ = size of the image </li></ul>
  52. 52. V Mirror C For Concave Mirror Principal axis p f Object q F Image
  53. 53. Ray Diagram Method (RDM) <ul><li>For Concave mirror: </li></ul><ul><ul><li>First Ray – Parallel to the axis, reflects to the mirror, then passing through focal point. </li></ul></ul><ul><ul><li>Second Ray – Passing through the focal point, reflect to the mirror, then parallel to the axis. </li></ul></ul><ul><ul><li>Third Ray – Passing through center of curvature, then bounce back. </li></ul></ul>
  54. 54. RDM V Mirror C Principal axis Y F Image 1 st Ray 2 nd Ray 3 rd Ray Object Concave Mirror
  55. 55. Problem Solving: <ul><li>A 3.0 cm tall light bulb is placed a distance of 40 cm from a concave mirror having a focal length of 10.2 cm. Determine the image distance. </li></ul>
  56. 56. LENSES <ul><li>It is an optical system with two refracting surfaces. </li></ul>
  57. 57. Thin Lens <ul><li>Has two spherical surfaces close enough so its thickness can be neglected. </li></ul><ul><li>Types of Thin lens </li></ul><ul><ul><ul><li>Converging Lens </li></ul></ul></ul><ul><ul><ul><li>Diverging Lens </li></ul></ul></ul>
  58. 58. continuation: <ul><li>Converging Lens </li></ul><ul><ul><li>Different kinds of converging lens: </li></ul></ul>Meniscus Piano-convex Double-convex
  59. 59. continuation: <ul><li>Diverging Lens </li></ul><ul><ul><li>Different kinds of diverging lens: </li></ul></ul>Meniscus Piano-concave Double-concave
  60. 60. Parts of Lenses <ul><li>Optic axis </li></ul><ul><ul><li>The central horizontal line defined by the centers of curvature of the two spherical surfaces. </li></ul></ul><ul><li>Focal points (F 1 and F 2 ) </li></ul><ul><li>Focal Length (f) </li></ul><ul><ul><li>Distance between a focal point and the center of the lens </li></ul></ul><ul><ul><li>The two focal lengths are always equal for a thin lens </li></ul></ul>
  61. 61. continuation: <ul><li>Image Formation by thin lenses </li></ul><ul><ul><li>Real image are located on the side of the lens opposite that of the object. </li></ul></ul><ul><ul><li>Virtual images are located on the same side of the lens as the object </li></ul></ul>
  62. 62. Converging lens F 1 F 2 f f Optic axis
  63. 63. continuation: <ul><li>When a beam of parallel rays pass through the lens, the rays converge at one focal point. </li></ul><ul><li>Its focal length is defined to be positive. </li></ul>F 2 F 1 f f F 2 F 1 f f Optic axis Optic axis
  64. 64. <ul><li>Converging lens can form either real or virtual image. </li></ul><ul><li>Real image if the distance of the object from the center of the lens is greater than the focal length (p>f). </li></ul><ul><li>Virtual image if the distance of the object from the center of the lens is less than the focal length (p<f). </li></ul>Image formation by Thin Lenses
  65. 65. Real Image F 1 F 2 Object Image f f p q Optic axis
  66. 66. Virtual Image F 1 Object F 2 f f Image p q Optic axis
  67. 67. Diverging lens F 1 F 2 f f Optic axis
  68. 68. continuation: <ul><li>When a beam of parallel rays are incident on this lens, the rays diverge after refraction. </li></ul><ul><li>Its focal length is defined to be negative. </li></ul>F 2 F 1 f f F 2 F 1 f f Optic axis Optic axis
  69. 69. Image formation by Thin Lenses F 1 F 2 Object Image f f p q The image formed by a diverging lens is always virtual. Optic axis
  70. 70. Lens Equation Thin Lens equation: Lateral magnification:
  71. 71. Problem Solving: <ul><li>A converging lens has a focal length of 12.0 cm for an object 20.0 cm to the left of the lens, </li></ul><ul><ul><li>Determined: </li></ul></ul><ul><ul><ul><li>The image position </li></ul></ul></ul><ul><ul><ul><li>The image magnification </li></ul></ul></ul>
  72. 72. Lenses and Mirror <ul><li>Assignment: </li></ul><ul><li>Computerized, Short bond paper </li></ul><ul><ul><li>Research work </li></ul></ul><ul><ul><ul><li>The Eye </li></ul></ul></ul><ul><ul><ul><li>The Camera </li></ul></ul></ul><ul><ul><ul><li>The Magnifying Glass </li></ul></ul></ul><ul><ul><ul><li>The Telescope (Galileo) </li></ul></ul></ul><ul><ul><ul><li>The Microscope </li></ul></ul></ul>