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## Optics

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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 LGP16/LGP8 = 4 LGP 8 inch = p (8/2)2 A 16 inch telescope has 2800 X the LGP of the eye. LGP 16 inch/LGP eye (0.3inch) = (16/0.3)2 = 2844**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) length Amplitude (A) height Frequency (f) 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 = l f Frequency increasesFrequency decreases Energy increasesEnergy decreases Wavelength decreasesWavelength increases**An Electromagnetic Wave (a.k.a. Light)**Light travels at a velocity c = l f (3x108 m/s)**The Visible Spectrum**COLOR FREQUENCY (10-14 Hz) WAVELENGTH (nm) • R 4.0-4.8 750-630 • O 4.8-5.1 630-590 • Y 5.1-5.4 590-560 • G 5.4-6.1 560-490 • B 6.1-6.7 490-450 • V 6.7-7.5 450-400**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 = l f speed of light = wavelength x frequency c = 3 x 108 m/s E = hf = hc/l 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 Radiation Output**Solar Spectrum 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.”**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”**Two Slit Destructive Interference**• Path Length Difference = multiples of 1/2 l**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.**Resolving Power**Telescope diameter = D (cm) Resolution = a (arcminutes) a = 11.6/D Larger D = smaller angular sizes resolved**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