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Lecture 3 Optics and Telescopes The Telescopes of Mauna Kea Guiding Questions 1. Why is it important that telescopes be large? 2. Why do most modern telescopes use large mirrors rather than large lens? 3. Why are observatories in such remote locations? 4. How do astronomers use telescope to measure the spectra of distance objects? 5. Why do astronomers need telescopes that detect radio waves and other non-visible forms of light? 6. Why is it useful to put telescopes in orbit? Homework 3 FGK10: Chap 5, Q-43, 44; Chap 6, Q-24, 32, 38 NB: for Q-38 in Chap 6, first find HST’s resolution using information from Question 32. and A1: A telescope with an objective focal length of f1, and an eyepiece focal length of f2. The objective and the eyepiece are separated by the sum of their focal lengths f1+f2. Show that the angular magnification of the telescope is given by f1/f2. 3.1 refracting and reflecting telescopes • A lens or mirror changes the direction of light to concentrate incoming light at a focus and form an image of the light source at the focal plane. • Telescopes using lens are refractors, and those using mirrors are reflectors. A mirror reflects light to form an image. A lens refracts light to make an image. A human eye is a lens. A refracting telescope uses a large diameter objective lens with a long focal length to form an image and a small eyepiece lens with a short focal length to magnify the image. f2 f1 In modern astronomy, a CCD (charge-coupled device) camera replaces the eyepiece and is placed at the focal plane to record observations in digital format. The largest refractor ever built since 1897, 102 cm (=1.02 m) diameter , 19.5 m focal length. Housed in Yerkes Observatory near Chicago. There are many designs of reflecting telescopes, mostly with a primary mirror and a secondary mirror. • Newtonian focus • Prime focus • Cassegrain focus • Coude focus Gemini North Telescope on Mauna Kea Most modern telescopes are reflectors. Problems with refractors: • Chromatic aberration: focal length varies with wavelength • Costly to make a large lens free of defects, such as bubbles • Light is absorbed and scattered in the glass • Heavy to support, distortion under weight Chromatic aberration Advantages of reflectors: • The mirror is made to be highly reflective. • Fewer problems with chromatic aberration, glass defects, support and distortion. • Spherical aberrations can be corrected. Spherical aberration The world’s largest telescopes are reflectors. The telescopes of Mauna Kea Observatory on La Palma From left to right, the William Herschel Telescope, Dutch Open Telescope, the Carlsberg Meridian Telescope, the Swedish Solar Telescope, the Isaac Newton Telescope (second from right) and the Jacobus Kapteyn Telescope (far right) at Roque de los Muchachos. (Photo by Bob Tubbs) European Southern Observatory (ESO) in Chile. (Copyright: R. Rekola) 3.2 Capabilities of a telescope The angular magnification is given by the ratio of the focal length of the objective lens/mirror to the focal length of the eye piece - objective lens/mirror of a longer focal length produce bigger (in what sense?) images: M ~ f1/f2 f1 Objective lens f2 Eye piece The light gathering power of a telescope is proportional to the area of the objective lens/mirror, which is proportional to the square of the lens/mirror diameter bigger telescopes produce brighter images. L D2 R 2σT 4 2 -1 2 P = Fobs A = π = π D (J s ) ∝ D 4 πd 2 4 4d 2 € Ex.1: The pupil size of the human eye is about 5mm, and its focal length is 17mm. The largest refractor ever built has a diameter of 102 cm and focal length of 19.5 m. (a) How many times greater is the light gathering power of this telescope compared to that of human eyes? (b) What’s the magnification of the telescope if the focal length of its eyepiece is the same as that of the human eye? ⎛ 102 cm ⎞2 ⎛ 1020 mm ⎞2 2 4 (a) ⎜ ⎟ = ⎜ ⎟ = 204 = 4.2 × 10 ⎝ 5 mm ⎠ ⎝ 5 mm ⎠ 19.5 m 195000 mm (b) = = 1.1 × 10 3 17 mm 17 mm € € The angular resolution of a telescope is limited by diffraction: bigger telescope, more details. Diffraction limited angular resolution: 5 λ θ = 2.5× 10 D θ = diffraction limited angular resolution, in arcsec λ = wavelength of light, in meters D = diameter of telescope objective, in meters The angular resolution of a telescope determines how much detail we may see in an image -- the angular resolution of human eyes is 1 arcmin, and all planets have angular size of or less than 1 arcmin. Ex.2: Diffraction limited angular resolution of Keck Telescopes (D = 10m): θ = 2.5x105 (550nm/10m) = 0.01 arcsec. Ex.3: To have 1 arcsec angular resolution by observing at microwave wavelength (3 cm), how big a mirror is needed? D = 2.5 x 105 (λ/θ) = 2.5x105 (0.03 m/1) = 7500 m (!) Aiming at large telescopes: the larger the aperture, the brighter is the image. the larger the aperture, the more details we can see… Q: shall we build telescopes of larger objective focal length to better resolve an image? 3.3 Atmosphere turbulence and light pollution In reality, telescope images are degraded by the blurring effects of the atmosphere and by light pollution. The angular resolution limited by the atmosphere turbulence is called seeing. Seeing varies at different locations. Telescopes are desirably operated at good-seeing sites (e.g. Mauna Kea, seeing = 0.5”). Ex.4: Big Bear Solar Observatory build on a mountain top (7000 feet) in the middle of a lake to minimize effects by smog, clouds, and atmosphere turbulence. The best seeing at this site is around 1”, i.e., one thousandths of the Sun’s radius. Q: limited by seeing, shall we operate big telescopes on the ground? Adaptive optics (AO) is a smart technique to compensate for the atmosphere turbulence by deforming the flexible mirror controlled by a very powerful computer and fast-acting mechanical devices. Ex.6: Applying adaptive optics to retrieve high resolution observations of a sunspot. Ex.5: Observing Neptune without and(Image withCredit: AO. Philip Lau) By National Optical Astronomical Observatory Adaptive optics (AO) uses a deformable mirror to correct the distorted wave front by atmosphere turbulence. Image credit: http://subarutelescope.org 3.4 Spectrograph Spectroscopy is one of the most important parts of observational astronomy. Spectral observations can tell us the temperature, chemical composition, and motion of remote celestial objects. A prism spectrograph Ex.7: Spectral observations of the Sun. Ex.8 Hα line observed in the Sun’s atmosphere. Hα line Ex.9: Dopplergram showing oscillations in the Sun’s photosphere. 3.5 Interferometry - radio telescopes Radio telescopes make images with interfering radio signals from many radio telescopes separated by many kilometers. The distance between the telescopes is a baseline. The longer the baseline, the higher the resolution. θ ~ λ → λ D b The Very Large Array (VLA, New Mexico) consists of 27 €radio telescopes. Radio Jupiter Credit: I. de Pater (UC Berkeley) NRAO, AUI, NSF Ex.10: Radio Jupiter recorded at VLA, New Mexico. The radio waves mapped in this false-color image are produced by energetic electrons trapped within Jupiter's intense magnetic field. The radio emitting region extends far beyond Jupiter's cloud tops and surrounds Jupiter. While it glows strongly at radio wavelengths, Jupiter's radiation belt is invisible in the more familiar optical and infrared views which show the Jovian cloud tops and atmospheric features in reflected sunlight. NB: this type of radio emission is a non-thermal emission, different from blackbody continuum radiation or line emission. 3.6 Space telescopes Telescopes in orbit are free of atmosphere turbulence and can observe at wavelengths to which the Earth’s atmosphere is opaque. The atmosphere is transparent in three wavelength regions, optical window, radio window, and some parts of near infrared. Telescopes in the space can observe dusts around stars and galaxies in infrared, hot stars and gas, the Sun’s corona, and planets atmosphere in ultraviolet and X-rays, and some very energetic phenomena in γ-rays. The Hubble Space Telescope (HST) launched in 1990 had a 2.4-meter objective mirror and was designed to observe at wavelengths from 115 nm (ultraviolet) to 1µm (infrared). HST uses a CCD to record images. HST has made numerous discoveries. The James Webb Space Telescope (JWST) to be launched soon will have a 6.5m diameter objective mirror, and observe from 600nm to 28 µm. (http://www.jwst.nasa.gov/) ROSAT ASCA X-ray telescopes The Compton Gamma Ray Observatory (CGRO) detect Gamma ray and hard X-ray bursts. TRACE RHESSI Ultraviolet, X-ray, and Gamma ray space telescopes observing the Sun. The entire sky at five wavelength ranges: visible, radio, infrared (IRAS), X-ray (ROSAT), and gamma-ray (CGRO) showing different structures of the Milky Way and beyond. Key Words • • • • • • • • • • • adaptive optics angular resolution baseline chromatic aberration chemical composition diffraction focal length focal plane interferometry magnification objective lens • • • • • • • • objective mirror optical telescope radio telescope reflecting telescope (reflector) refracting telescope (refractor) seeing spectrograph spherical aberration Summary: Refracting telescopes (refractors) form images by bending light rays to a focus point through glass lens. They have shortcomings like chromatic aberration, glass defects, and distortion by weight. Reflecting telescopes (reflectors) form images by reflecting light rays to the focus from curves mirrors, most used in modern astronomy. Theoretically, a telescope’s diffraction limited angular resolution depends on the diameter of the objective and observing wavelength. Atmosphere turbulence and light pollution blur telescope images. Adaptive optics can be applied to ground-based telescopes to correct the atmospheric distortion. Radio telescopes use interferometry techniques to achieve high resolution images. Telescopes in space are free from the Earth’s atmosphere turbulence and are able to observe light at wavelengths - infrared, ultraviolet, X-ray, and gamma-ray - blocked by the atmosphere. References: FK Chap 6. & Lecture notes Star trails above Mauna Kea (Peter Michaud, Gemini Observatory)