Ch 6: Light and Telescope Wave and Wavelength..\..\aTeach\PhET\wave-on-a-string_en.jar Wavelength, Frequency and Speed Wave and Wavelength A wave is a disturbance that moves through a medium or through empty space. Wavelength is the distance between successive crests or trough of the wave. Wavelength, Frequency and Speed 1 second later The frequency, f, is the rate at which wavecrests pass a fixed point. Unit of f is Hz. This wave travels 4 wavelengths away in 1 second. Speed of wave is v f Think, Answer; Talk to your neighbors, Answer Two waves have the same speed. Wave A has four times the frequency of wave B. How does the wavelength of wave A compares with that of wave B? A) wavelength of wave A is 4 times that of B. B) wavelength of wave A is 1/4 times that of B. C) wavelength of wave A = wavelength of B. D) wavelength of wave A is 2 times that of B. E) wavelength of wave A is 1/2 times that of B. Recall: Speed of wave is v f 1
An Electromagnetic Wave Electromagnetic waves are oscillating electric and magnetic fields produced by accelerating electric charges. Flux E Electric field B Magnetic field Speed of EM wave c = 3 X 10 8 m/s. An example of air flux. Electromagnetic Flux The energy flux of a wave is the rate at which the wave carries energy through a given area. Prob 7: Saturn is ten times as far from the Sun as is the Earth. How does the flux of solar energy at Saturn compare with that at the Earth? E Flux, F 4 d 2 Electromagnetic Spectrum Electromagnetic Spectrum and their sources on Earth and in Cosmos Energy increases with increasing frequency. 2
Hydrogen Spectrum of Elements Emission Line Spectrum Each type of atom has a unique spectral fingerprint. A thin or low-density cloud of gas emits light only at specific wavelengths that depend on its composition and temperature, producing a spectrum with bright emission lines. Origin of Spectrum Energy levels of hydrogen Each type of atom has a unique set of energy levels. Each transition corresponds to a unique photon energy, frequency, and wavelength. Doppler Effect It is a change in the frequency and wavelength of a wave that is emitted by or reflected from a body in motion with respect to the observer. relative change speed v r c 0 original Shifts and motion Stationary Moving away Away faster Prob 9: Radio waves from a stars are observed at a wavelength of 20.02 cm. If the star and the Earth were motionless with respect to each other, the radio waves would have a wavelength of 20 cm. Are the star and the Earth moving towards each other? How fast are they moving toward or away? Moving toward Toward faster We generally measure the Doppler effect from shifts in the wavelengths of spectral lines. 3
Light behaves as Wave and Particle Experiments show that light has a dual nature; it behaves as both a wave and a particle. Wave nature Particle nature Study of the Photoelectric Effect Experiments show: The energy of ejected electrons depends on the frequency of the incident light. The colors arises from the interference of light. Electrons emitted due to photoelectric effect Contradiction: Wave theory cannot explain the frequency dependence of the maximum kinetic energy. Study of the Photoelectric Effect Explanation: Each electron in the metal absorbs a whole photon: some of the energy is used to eject the electron and the rest goes into the energy of the electron. Energy of a photon is given by E hf where h is Planck s constant. 34 h 6.6 10 Js Prob 11: Photon A has twice the frequency of Photon B. How do the energies of the two photons compare? What have we learned? What is light? Light can behave like either a wave or a particle. A light wave is a vibration of electric and magnetic fields. Light waves have a wavelength and a frequency. Photons are particles of light. What is the electromagnetic spectrum? Human eyes cannot see most forms of waves. The entire range of wavelengths of wave is known as the electromagnetic spectrum. Reflection of light 4
Refraction of light Light bends when it passes from one medium to another. This phenomenon is called refraction. Example: Refraction at Sunset Refracting property of media is described by its Refractive Index. speed in vacuum RI speed in medium Sun appears distorted at sunset because of how light bends in Earth s atmosphere. Prob 12: The wavelength of EM wave is 3m, and its frequency is 10 8 Hz. What is the index of refraction? Given: Since, 3 m speed in vacuum RI speed in medium c f 8 3 10 m/s 8 10 Hz 3 m 1 8 f 10 Hz RI =? No unit. c v because, c = 3x10 8 m/s A dispersion occurs because the index of refraction depends on the wavelength of light. c RI f Larger wavelength means less bending and vice-versa. Dispersion Lens Focal length and Curvature Highly curved: short focal length 1 focal length = Curvature 2 Slightly curved: long focal length 5
Mirror Formation of Image by a lens Focusing by two flat mirrors Image Point object: Image is formed at focus. Focusing by Parabolic mirror Inverted image Extended object: Image is formed at focal plane. The focal plane is where light from different directions comes into focus. How does your eye form an image? Focusing Light Refraction can cause parallel light rays to converge to a focus. Image Formation How do we record images? Digital cameras detect light with charge-coupled devices (CCDs). The image behind a single (convex) lens is actually upside-down! A camera focuses light like an eye and captures the image with a detector. The CCD detectors in digital cameras are similar to those used in modern telescopes. 6
Optical Telescope f Telescope Magnification f The area of the objective lens determines the light gathering power and hence brightness of an image. o e Two most important properties of a telescope 1. Light-collecting area: Telescopes with a larger collecting area can gather a greater amount of light in a shorter time. a. A telescope s diameter tells us its lightcollecting area: 2 Area = π(diameter/2). b. The largest telescopes currently in use have a diameter of about 10 meters. 2. Angular resolution: Telescopes that are larger are capable of taking images with greater detail. Angular Resolution Angular Resolution The minimum angular separation that the telescope can distinguish Ultimate limit to resolution comes from interference of light waves within a telescope. Larger telescopes are capable of greater resolution because there s less interference. Angular Resolution The rings in this image of a star come from interference of light wave. Resolution of an Image Resolution describes the ability of a telescope to distinguish fine details in an image. High Resolution. Low Resolution Close-up of a star from the Hubble Space Telescope This limit on angular resolution is known as the diffraction limit. The angular diameter of the bright central spot is given by 250000 D diameter of objective lens 7
Want to buy your own telescope? Buy binoculars first (e.g., 7 35 mm) quick and easy to use, you get much more for the same money. Ignore magnification ( 650 powers sales pitch!). Important: aperture size, optical quality, portability. Consumer research: Astronomy, Sky & Telescope, Mercury, astronomy clubs. Two basic designs of telescopes Refracting telescope: focuses light with lenses Reflecting telescope: focuses light with mirrors Refracting Telescope Reflecting Telescope Refracting telescopes need to be very long, with large, heavy lenses. Reflecting telescopes can have much greater diameters. Most modern telescopes are reflectors. Mirrors in Reflecting Telescopes What do astronomers do with telescopes? Imaging: taking pictures of the sky Spectroscopy: breaking light into spectra Timing: measuring how light output varies with time Twin Keck telescopes on Mauna Kea in Hawaii Segmented 10-meter mirror of a Keck telescope 8
Imaging Astronomical detectors generally record only one color of light at a time. Several images must be combined to make full-color pictures. Imaging using waves other than light Astronomical detectors can record forms of wave our eyes can t see. Color is sometimes used to represent different energies of nonvisible light. Spectroscopy Spectroscopy Graphing relative brightness of light at each wavelength shows the details in a spectrum. A spectrograph separates the different wavelengths of light before they hit the detector. Timing How does Earth s atmosphere affect ground-based observations? The best ground-based sites for astronomical observing are: calm (not too windy) high (less atmosphere to see through) dark (far from city lights) dry (few cloudy nights) A light curve represents a series of brightness measurements made over a period of time. 9
Light Pollution Twinkling and Turbulence Bright star viewed with ground-based telescope Same star viewed with Hubble Space Telescope Scattering of human-made light in the atmosphere is a growing problem for astronomy. Turbulent air flow in Earth s atmosphere distorts our view, causing stars to appear to twinkle. Adaptive Optics Calm, High, Dark, Dry The best observing sites are atop remote mountains. Without adaptive optics With adaptive optics Rapidly changing the shape of a telescope s mirror compensates for some of the effects of turbulence. Summit of Mauna Kea, Hawaii Why do we put telescopes into space? Transmission in Atmosphere Only radio and visible light pass easily through Earth s atmosphere. We need telescopes in space to observe other forms. 10
How can we observe invisible web? A standard satellite dish is essentially a telescope for observing radio waves. Radio Telescopes A radio telescope is like a giant mirror that reflects radio waves to a focus. Arecibo radio telescope in Puerto Rico. Infrared and Ultraviolet Telescopes X-Ray Telescopes X-ray telescopes also need to be above the atmosphere. SOFIA Spitzer Infrared and ultraviolet light telescopes operate like visible-light telescopes but need to be above atmosphere to see all wavelengths. Chandra X-Ray Observatory X-Ray Telescopes Gamma-Ray Telescopes Focusing of X-rays requires special mirrors. Mirrors are arranged to focus X-ray photons through grazing bounces off the surface. Fermi Gamma-Ray Observatory Gamma-ray telescopes also need to be in space. Focusing gamma rays is extremely difficult. 11
How can multiple telescopes work together? Interferometry Interferometry is a technique for linking two or more telescopes so that they have the angular resolution of a single large one. Interferometry Future of Astronomy in Space? Very Large Array (VLA) Easiest to do with radio telescopes. Now possible with infrared and visible-light telescopes. The Moon would be an ideal observing site. What have learned? How can we observe invisible wave? Telescopes for invisible wave are usually modified versions of reflecting telescopes. Many of the telescopes used for observing invisible light are in space. How can multiple telescopes work together? Linking multiple telescopes using interferometry enables them to produce the angular resolution of a much larger telescope. 12