Human Retina. Sharp Spot: Fovea Blind Spot: Optic Nerve

Transcription

1

2 I am Watching YOU!!

3 Human Retina Sharp Spot: Fovea Blind Spot: Optic Nerve

4 Human Vision An optical Tuning Fork

5 Optical Antennae: Rods & Cones Rods: Intensity Cones: Color

6 Where does light actually come from? Light comes from the acceleration of charges.

7 Light is emitted when an electron in an atom jumps between energy levels either by excitation or collisions.

8 Atoms are EM Tuning Forks They are tuned to particular frequencies of light energy.

9 Atomic Emission of Light Each chemical element produces its own unique set of spectral lines when it burns

10 Light Emission

11 Hydrogen Spectra

12 Helium Spectra

13 Mercury Spectra

14 Light Waves c E = Emax cos (kx ωt) B = Bmax cos (kx ωt) v E 1 = = B μ0ε0 Speed of Light in a vacuum: = c/ n 186,000 miles per second 300,000 kilometers per second 3 x 10^8 m/s

15 The Electromagnetic Spectrum v = λ f

16 Light Rays: Ignore Diffraction and Interference of waves! Diffraction depends on SLIT WIDTH: the smaller the width, relative to wavelength, the more bending and diffraction. We will assume that λ<<d, where d is the diameter of the opening. This approximation is good for the study of mirrors, lenses, prisms, etc.

17 We can consider light waves to be RAYS because if the object it interacts with are several times larger than the wavelength of light, it acts like it travels in straight lines and acts like a ray.

18 Ray Approximation The rays are straight lines perpendicular to the wave fronts With the ray approximation, we assume that a wave moving through a medium travels in a straight line in the direction of its rays

19 Reflection & Refraction θ i = θ r n sinθ = n sinθ

20 Why does a mirror reflect light? Mirrors are metallic (conductors) and have free electrons. These free electrons can absorb and re-emit a continuous spectrum of EM frequencies and so more of the incident light is reflected back and not absorbed by the material. Why does polishing a mirror make it more reflective?

21 Why are some materials Transparent? If the frequency of incident light resonates with the electron energy levels in the atom, then the atoms absorb the light and re-emit but not always at the same frequency or in the same direction. UV is absorbed and emitted as IR. Visible light passes through.

22 Why are some materials Opaque? Atoms absorb light which goes into vibrational energy or is re-emitted as infrared (heat)

23 Why are some materials colored?

24 RGB Color Theory

25 If you pass white light through a prism, it separates into its component colors. long wavelengths R.O.Y. G. B.I.V short wavelengths

26 The speed and wavelength change but the FREQUENCY does NOT. Fr Frequency depends on the oscillating source! long wavelengths R.O.Y. G. B.I.V short wavelengths

27 Why are some materials colored? Colored materials absorb certain colors that resonate with their electron energy levels and reject & reflect those that do not.

28 Why is the Sky Blue? Air molecules are tuned to blue light which is absorbed and scattered in all directions. Red and Green (yellow) light pass through unabsorbed.

29 Law of Reflection θ i = θ r

30 How many times will the incident beam shown be reflected by each of the parallel mirrors?

31 What is the smallest mirror that you can see your entire image in? 1. As tall as you 2. Longer than you 3. Shorter than you 4. Depends on distance to the mirror. 5. Depends on where it is hung

32 How long does a mirror have to be to see your entire image in? Suppose a woman stands in front of a mirror as shown. Her eyes are 1.65 m above the floor, and the top of her head is 0.13 higher. Find the height above the floor of the top and bottom of the smallest mirror in which she can see both the top of her head and her feet. How is the distance related to the woman s height?

33 Refraction: Bending Light into Focus

34 Refraction: Bending of Light Transmitted through Materials

35 Light Bends because it Slows Down.

36 Atoms are Optical Tuning Forks If the frequency of incident light resonates with the electron energy levels in the atom, then the atoms absorb and re-emit the light, and that takes time.

37 Light refracts toward the normal when it slows down (air to water) and refract away from the normal when it speeds up (water to air)

38 Principle of Least Time (How does light know how to do this?)

39 Index of Refraction n = c v n 1 Vacuum: 1 Water: 1.33 Glass: 1.46 Diamond: 2.4

40 Snell s Law of Refraction Angles are always measured from the normal. n sinθ = n sinθ

41 Snell s Law Example Light is refracted into a crown glass slab θ 1 = 30.0 o, θ 2 =? n 1 = 1.00 and n 2 = 1.52 θ 2 = sin -1 (n 1 / n 2 ) sin θ 1 = 19.2 o The ray bends toward the normal, as expected

42 A light ray travels from medium 1 to medium 3 as shown. For these media, A. n 3 < n 1. B. n 3 = n 1. C. n 3 > n 1. D. We can t compare n 1 to n 3 without knowing n 2.

43 A light ray travels from medium 1 to medium 3 as shown. For these media, A. n 3 < n 1. B. n 3 = n 1. C. n 3 > n 1. D. We can t compare n 1 to n 3 without knowing n 2.

44 Sample Fun Refraction Problem

45 The Index of Refraction The speed of light in any material is less than its speed in vacuum The index of refraction, n, of a medium can be defined as speed of light in a vacuum c n = speed of light in a medium v n λ λin vacuum = λn λin a medium

46 Frequency Doesn t Change! 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

47 Refraction: Apparent Depth A person spearfishing from a boat sees a stationary fish a few meters away in a direction about 30 degrees below the horizontal. To spear the fish (assuming it doesn t change direction when it enters the water), should the person aim? a) above where he sees the fish b) precisely at the fish? c) below the fish?

48 Possible Beam Directions Possible directions of the beam are indicated by rays numbered 1 through 5 The refracted rays are bent away from the normal since n 1 > n 2

49 Total Internal Reflection θ = 90 o 2 n sinθ = n sinθ sinθ = C n n 2 1 The Critical Angle

50 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 A flexible light pipe is called an optical fiber A bundle of parallel fibers (shown) can be used to construct an optical transmission line Fiber Optics

51 Critical Angle Sample Problem A ray of light, emitted by a laser located beneath the surface of an unknown liquid with air above it, undergoes total internal refection as shown. What is the index of refraction for the liquid? Wht is its likely identification?

52 If you pass white light through a prism, it separates into its component colors. long wavelengths R.O.Y. G. B.I.V short wavelengths

53 The index of refraction depends on WAVELENGTH. long wavelengths R.O.Y. G. B.I.V short wavelengths

54 The speed and wavelength change but the FREQUENCY does NOT. Fr Frequency depends on the oscillating source! long wavelengths R.O.Y. G. B.I.V short wavelengths

55 Why does Violet Light bend more than Red Light? Violet light slows down more because the atoms in the material are tuned to higher frequencies. As the violet light travels through glass it takes more time to be absorbed and re-emitted.

56 Variation of Index of Refraction with Wavelength The index of refraction for a material generally decreases with increasing wavelength Violet light bends more than red light when passing into a refracting material

57 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

58 Angle of Deviation The ray emerges refracted from its original direction of travel by an angle δ, called the angle of deviation The angle of deviation depends on the wavelength

59

60 How are Rainbows Formed?

61 Dispersion: Raindrops Act like Prisms 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

62 Another Way to Bend Waves

63 Diffraction depends on SLIT WIDTH: the smaller the width, relative to wavelength, the more bending and diffraction.

64 Superposition Waves ADD in space.

65 Constructive: l l = mλ, m= 0,1,2,3,

66 1 Destructive: l2 l1 = ( m+ ) λ, m= 0,1,2,3,... 2

67

68 Single Slit Diffraction Depends on Slit Width λ Dark fringe: sin θ = m m= 1, 2,3,... W

69 Double Slit is VERY IMPORTANT because it is evidence of waves. Only waves interfere like this.

70 Proof Light is a Wave!

71 Constructive: Δ l = l l = mλ, m= 0,1,2,3, Destructive: Δ l = l2 l1 = ( m+ ) λ, m= 0,1,2,3,... 2

72 Constructive: Δ l = l l = mλ, m= 0,1,2,3, Δ l = dsinθ λ Bright fringe: sin θ = m m= 0,1,2,3,... d Δl

73 λ Bright fringe: sin θ = m m= 0,1,2,3,... d 1 λ Dark fringe: sin θ = ( m+ ) m= 0,1, 2,3,... 2 d Where m is the order of the interference. Δl

74 Red light (λ=664nm) is used in Young s double slit as shown. Find the distance y on the screen between the central bright fringe and the third order bright fringe. λ Bright fringe: sin θ = m m= 0,1,2,3,... d

75 Single Slit vs Double Slit The light curve of a multiple slit arrangement will be the interference pattern multiplied by the single slit diffraction envelope. This assumes that all the slits are identical.

76 Combined Effects This pattern is a close up of the central bright fringe.

77 Double Slit for Electrons shows Wave Interference

78 Dispersion via Diffraction constructive : d sin θ = mλ, m = 0,1, 2,3

79 Diffraction Gratings constructive : d sin θ = mλ, m = 0,1, 2,3 Note: The greater the wavelength, the greater the angle. How does this compare to dispersion with a prism?

80 Dispersion: Diffraction Gratings How does this compare to dispersion with a prism? Longer wavelength light is bent more with a grating. Shorter wavelength light is bent more with a prism.

81 Hydrogen Spectra

82 Helium Spectra

83 Mercury Spectra

84 Neon Spectrum

85 Oxygen Spectrum

86 Argon Spectrum

87

88 Absorption Spectrum of Hydrogen Gas

89 Cosmological Redshift: Expanding Universe Stellar Motions: Rotations and Radial Motions Solar Physics: Surface Studies and Rotations Gravitational Redshift: Black Holes & Lensing Exosolar Planets via Doppler Wobbler

90 Spectral lines shift due to the relative motion between the source and the observer

91 Red Shift: Moving Away Blue Shift: Moving Toward

92 A mixture of violet light (410 nm in vacuum) and red light (660 nm in vacuum) fall on a grating that contains 1.0 x10 4 lines/cm. For each wavelength, find the angle and the distance from the central maximum to the first order maximum.

93 Diffraction Grating Problem White light is spread out into spectral hues by a diffraction grating. If the grating has 1000 lines per cm, at what angle will red light (l = 640 nm) appear in first order? a b c d e. 1.84

94 Circularly Polarized EM Wave

95 Elliptically Polarized EM Wave

96 Polarization of Light Plane Polarized Circular Polarized Polarization upon Reflection

97 Polarization of Light A wave is said to be linearly polarized if the resultant electric field E vibrates in the same direction at all times at a particular point The plane formed by E and the direction of propagation is called the plane of polarization of the wave

98 Methods of Polarization It is possible to obtain a linearly polarized beam from an unpolarized beam by removing all waves from the beam except those whose electric field vectors oscillate in a single plane Processes for accomplishing this include selective absorption reflection double refraction scattering

99 Polarization by Selective Absorption The most common technique for polarizing light Uses a material that transmits waves whose electric field vectors lie in the plane parallel to a certain direction and absorbs waves whose electric field vectors are perpendicular to that direction

100 Intensity of Polarized Light, Examples On the left, the transmission axes are aligned and maximum intensity occurs In the middle, the axes are at 45 o to each other and less intensity occurs On the right, the transmission axes are perpendicular and the light intensity is a minimum

101 If the filters are perpendicular no light gets through.

102 Malus Law I = I cos 2 θ 0

103 Polarization I = I cos 2 θ 0 The intensity of unpolarized light passing through a polarizer will be reduced my ½, because the average value of the cosine squared term over all directions is ½.

104 If the incident beam is linearly polarized along the vertical direction and has an intensity of 50 W/m 2 and the angle is 30 degrees, which set up transmits more light? Determine the average intensity of the transmitted beam for both setups. If the light is unpolarized, which set up transmits the most light?

105 Polarization Problem Unpolarized light is passed through three successive Polaroid filters, each with its transmission axis at 45 to the preceding filter. What percentage of light gets through? a. 0% b. 12.5% c. 25% d. 50% e. 33%

106 Polarization by Reflection When an unpolarized light beam is reflected from a surface, the reflected light may be Completely polarized Partially polarized Unpolarized It depends on the angle of incidence If the angle is 0, the reflected beam is unpolarized For other angles, there is some degree of polarization For one particular angle, the beam is completely polarized

107 Polarization by Reflection, Partially Polarized Example Unpolarized light is incident on a reflecting surface The reflected beam is partially polarized The refracted beam is partially polarized

108 Polarization by Reflection, Completely Polarized Example Unpolarized light is incident on a reflecting surface The reflected beam is completely polarized The refracted beam is perpendicular to the reflected beam The angle of incidence is Brewster s angle

109 Polarization by Reflection The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, θ p Brewster s law relates the polarizing angle to the index of refraction for the material sin θp n = = tan θp cos θ p θ p may also be called Brewster s angle

110 Brewster s Angle sin θp n = = tan cos θ Sunlight reflected from a smooth ice surface is completely polarized. Determine the angle of incidence. (nice = 1.31.) a.52.6 b.25.6 c d.56.2 e p θ p

111 Which pair of glasses will cut glare from light reflected from the road?

112 Polarization by Double Refraction: Birefringence In certain crystalline structures, the speed of light is not the same in all directions Such materials are characterized by two indices of refraction They are often called double-refracting or birefringent materials

113 Birefringent Materials These calcite crystals are a birefringent medium, so they split one light beam into two beams. There are different indices of refraction for different polarizations. In p polarization, n= and in s polarization n= Placed on text, images appears double.

114 3D Movies Stereoscopic photos and movies, popularily known as 3D, are made with two cameras, each recording an image for each eye. Consequently, true color stereo requires two projectors to shine on the screen. With a separate image for each eye, one can see depth. Images 'float' right out of the screen in front of your face.

115 Dispersion Sample Problem The index of refraction for violet light in silica flint glass is 1.66, and that for red light is What is the angular dispersion of visible light passing through a prism of apex angle 60.0 if the angle of incidence is 50.0? red (660 nm) violet (410 nm)