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Optics • Read Your Textbook: Foundations of Astronomy – Chapter 6, 7 • Homework Problems Chapter 6 – Review Questions: 1,2 5-7 – Review Problems: 1-3, 8 – Web Inquiries: 2 • Homework Problems Chapter 7 – Review Questions:1, 2, 4, 5, 7, 10-12 – Review Problems: 1-4, 9 – Web Inquiries: 1 Light Gathering Power Light Gathering Power Telescope diameter (D) Light Gathering Power (LGP) is proportional to area. LGP = p (D/2)2 D = diameter Light Gathering Power Light Gathering Power Telescope diameter (D) Light Gathering Power (LGP) is proportional to area. LGP = p (D/2)2 D = diameter A 16 inch telescope has 4 X the LGP of an 8 inch. LGP 16 inch = p (16/2)2 LGP 8 inch = p (8/2)2 LGP16/LGP8 = 4 A 16 inch telescope has 2800 X the LGP of the eye. LGP 16 inch/LGP eye (0.3inch) = (16/0.3)2 = 2844 More Light Types of Waves • Compression wave oscillations are in the direction of motion • Transverse Wave oscillations are transverse to the direction of motion Wave Parameters Wavelength (l) Amplitude (A) Frequency (f) length height repetition Amplitude: Size of wave (perpendicular to direction of propagation) Proportional to Intensity(Sound loudness, Light brightness) Wavelength: l Size of wave (in the direction of propagation) Frequency: Number of waves passing a fixed position per second f (cycles/second, Hertz) Wave Speed: v=lf Frequency increases Energy increases Wavelength decreases Frequency decreases Energy decreases Wavelength increases An Electromagnetic Wave (a.k.a. Light) Light travels at a velocity c = l f (3x108 m/s) E-M Frequency and Wavelength Electromagnetic Spectrum Electromagnetic Spectrum Uses The Visible Spectrum COLOR FREQUENCY (10-14 Hz) WAVELENGTH (nm) • • • • • • 4.0-4.8 4.8-5.1 5.1-5.4 5.4-6.1 6.1-6.7 6.7-7.5 R O Y G B V 750-630 630-590 590-560 560-490 490-450 450-400 Radio (Light) Wave 94.1 THE POINT, broadcasts at a frequency of 94.1 MHz (106 Hz). What is the wavelength of its carrier wave? A radio wave is a light wave, c = l f Radio (Light) Wave 94.1 THE POINT, broadcasts at a frequency of 94.1 MHz (106 Hz). What is the wavelength of its carrier wave? A radio wave is a light wave, c = l f l = 3 x 108/94.1 x 106 = 3.2 meters Doppler Effect Change in frequency of a wave due to relative motion between source and observer. A sound wave frequency change is noticed as a change in pitch. http://pls.atu.edu/physci/physics/people/trantham/applets/doppler/javadoppler.html Doppler Effect for Sound • Change in frequency of a wave due to relative motion between source and observer. Line of Sight Only sensitive to motion between source and observer ALONG the line of sight. Radial Velocity Convention True Velocity Radial = Line of Sight Component Observer Radial Velocity > 0 Moving Away No Doppler Shift Transverse motion Radial Velocity < 0 Moving Toward Doppler Effect • Light Doppler Effect for Light Waves • Change in frequency of a wave due to relative motion between source and observer. • c=lf E = hf = hc/l speed of light = wavelength x frequency c = 3 x 108 m/s energy of a light wave, a photon of frequency (f) or wavelength (l) h = planck’s constant 6.63 x 10-34 J-sec A light wave change in frequency is noticed as a change in “color”. Wavelength Doppler Shift l0 = at rest (laboratory) wavelength l = measured (observed) wavelength Dl = l - l0 = difference between measured and laboratory wavelength vr/c = Dl/l0 vr = (Dl/l0)c radial velocity Solar Spectrum Solar Radiation Output The sun looks “yellow” Wien’s Law Wien's law relates the temperature T of an object to the wavelength maximum at which it emits the most radiation. Mathematically, if we measure T in kelvins and the wavelength maximum (l) in nanometers, we find that* lmax = 3,000,000/T *3,000,000 is an approximation of the true value 2,900,000 (just like 300000000 m/s approximates the speed of light 299792458. Approximate Solar Peak lmax = 3,000,000/T Tsurface = 5800 K (solar surface temperature) lmax = 3,000,000 / 5800 K = 517 nm (Yellow-Green) The atmosphere scatters most of the blue light making the sun appear more yellow and the sky blue Light Waves • Light is a wave that propagates at speed c. – c = 3 x 108 m/s in a vacuum – velocity is slower in other media • Like sound waves and other waves, light should exhibit the same properties seen for other waves. These are diffraction, reflection, and interference. • In addition, light waves also exhibit refraction, dispersion and polarization. Diffraction of Water Waves • Diffraction: Waves ability to bend around corners Ray Trace A ray trace is meant to represent the direction of propagation for a set of parallel waves called a “wave front.” Diffraction Constructive Interference • Waves combine without any phase difference • When they oscillate together (“in phase”) Wave Addition Amplitude ~ Intensity Destructive Interference • Waves combine differing by multiples of 1/2 wavelength • They oscillate “out-of-phase” Wave Subtraction Two Slit Destructive Interference • Path Length Difference = multiples of 1/2 l Two Slit Interference Two Slit Interference • Slits are closer together, path length differences change Light or Dark? • Path Length Differences = l, Waves arrive in phase • Path Length Differences = 1/2 l, Waves arrive out of phase Light or Dark? Light from the slits arrives at A. Path Length from slit 1 is 10,300 nm and from slit 2 is 10,300 nm for a difference of 0 nm. There is no path length difference so the waves from the two slits arrive at A oscillating in phase. They add constructively and produce a brighter area. Light or Dark? Light from the slits arrives at E. Path Length from slit 1 is 10,800 nm and from slit 2 is 11,800 nm for a difference of 1000 nm. This path length difference is exactly two wavelengths so the waves from the two slits arrive at E oscillating in phase. They add constructively and produce a brighter area. Light or Dark? Light from the slits arrives at B. Path Length from slit 1 is 10,450 nm and from slit 2 is 10,200 nm for a difference of 250 nm. This path length difference is exactly 1/2 a wavelength so the waves from the two slits arrive at B oscillating out of phase. They add destructively and produce a dark area. Newton’s Rings Resolution Resolving Power Telescope diameter = D (cm) Resolution = a (arcminutes) a = 11.6/D Larger D = smaller angular sizes resolved Increasing Resolving Power Magnification Telescope diameter (D) Focal Length (f) f/# The focal length is # times the objective diameter Magnification = focal length of objective/ focal length of eyepiece f-number (f/#) The f/# refers to the ratio of the focal length to the diameter. An f/10 optical system would have a focal length 10 X bigger than its diameter. The f/10 celestron C8 has a focal length of 80 inches. (8 inch aperture times 10) Our 16 inch telescope in the newtonian f/4 configuration has a focal length of 64 inches (16 x 4). Magnification Magnification depends on the ratio of the focal lengths for the primary aperture to the eyepiece. M = focal length of objective / focal length of eyepiece = fo/fe Therefore for the same eyepiece, in general, the telescope with the longest focal length can achieve the greater magnification. Magnification Isn’t Everything Magnifying something spreads the light out into a larger and larger area. An object is only so bright and magnifying an image too much causes it to become so diffuse that it ceases to be visible. Magnifying power for a telescope is not what you are looking for. Besides, increased magnification can be achieved by changing eyepieces. What do you want in a telescope? Resolving Power Telescope diameter = D (cm) Resolution = a (arcminutes) a = 11.6/D Larger D = smaller angular sizes resolved The Principle of Reflection The Angle of Incidence = The Angle of Reflection Reflection Optical Mirrors Reflection Telescope Configurations Imaging Interactive Demonstrations On The WEB • Simple Geometric Optics http://pls.atu.edu/physci/physics/people/trantham/Applets/lenses/javalens.html • Wave Addition http://pls.atu.edu/physci/physics/people/trantham/Applets/waveaddition/waveapplet.htm l • Two-slit Interference http://pls.atu.edu/physci/physics/people/trantham/Applets/youngslit/javayoungslit.html • Doppler Shift http://pls.atu.edu/physci/physics/people/trantham/Applets/Doppler/javadoppler.html Refraction Refraction: The bending of light upon entering a medium with with a different density. A light wave will speed up or slow down in response to a changing medium. Refraction is Dispersive Light of different frequencies is refracted by different amounts Beach Party Pavement Sand Beach Party Pavement Sand Beach Party Pavement Sand Beach Party Pavement Sand Beach Party Pavement Sand Refraction Light waves, like people wave fronts can slow down also. Bending Because of Velocity Principle of Refraction: A light wave will slow down upon entering a denser medium. The refracted light will be bent toward the normal to the surface in this case. A light wave will speed up upon entering a less dense medium. The refracted light will be bent away from the normal to the surface in this case. Refraction Velocity slows down and is bent toward the normal to the surface, then speeds up upon exiting the glass and is bent away. Air Glass Index of Refraction To characterize the change in velocity of a light wave in a transparence medium, we use the index of refraction (n). It is the ratio of the speed of light in a vacuum (c) compared to the speed of light in the medium (v). n=c/v Note: since c = 3x108 m/s is the speed limit for light, v for any other medium is less than c. Therefore, the index of refraction is always > 1.0 Indices of Refraction transparent medium vacuum air water ice salt Pyrex glass quartz glycerine acrylic diamond index of refraction 1.0000000 1.00029 1.33 1.31 1.54 1.50 1.46 1.47 1.70 1.24 Light Speed What is the speed of light waves traveling through acrylic? nacrylic = c / v Light Speed What is the speed of light waves traveling through acrylic? nacrylic = c / v 1.7 = 3x108/v V = 3x108/1.7 = 1.76x108 m/s Light Speed What is the index of refraction for a substance in which the speed of light is only 2.0x108 m/s? nunknown = c / v = 3x108/2x108 = 1.5 This substance is, or most resembles….glass. Glass has an index of refraction of 1.50 Refracting and Reflecting Telescopes Lenses Refraction The Beauty of Dispersion and Refraction Rainbows Chromatic Aberration Formation of Images Hubble Space Telescope Hubble’s Innards Repairs and Instrument Upgrades New Instruments Hubble Images a-Ground based image b-Hubble before repair image c-Hubble before repair (image processing) image d-Hubble fixed image Instrumentation CCD Cameras Lasers Clock Drive Last but NOT least. You and telescopes are on the moving observatory we call earth. A clock drive is required to counter earth’s rotation and provide tracking for telescopes and cameras.