Optics and Telescopes
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1 PHYS 320 Lecture 6 Optics and Telescopes Jiong Qiu MSU Physics Department Wenda Cao NJIT Physics Department
2 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 parameters o distance objects? 5. Why do astronomers need telescopes that detect radio waves and other non-visible orms o light? 6. Why is it useul to put telescopes in orbit?
3 6.1 Optics - Thin Lens Formula Tracing a ew key rays 2 0 x x i = s s i = x x s s y y M i i i T = = =
4 Optics - Mirror Formula Under paraxial approximation, 2 0 x x i = s s i = x x s s y y M i i i T = = = 2 0 R i = =
5 6.2 Reracting and Relecting Telescopes A lens or mirror changes the direction o light to concentrate incoming light at a ocus and orm an image o the light source at the ocal plane. Telescopes using lens are reractors, and those using mirrors are relectors. A lens reracts light to make an image. A mirror relects light to orm an image. A human eye is a lens.
6 Reracting Telescope A reracting telescope uses a large diameter objective lens with a long ocal length to orm an image and a small eyepiece lens with a short ocal length to magniy the image. 2 1 In modern astronomy, a CCD (charge-coupled device) camera replaces the eyepiece and is placed at the ocal plane to record image in digital ormat.
7 The largest reractor ever built since 1897, 102 cm (=1.02 m) diameter, 19.5 m ocal length. Housed in Yerkes Observatory near Chicago. Angular size o the Sun is about 32 (arc-minute), could you ind the physical size at the ocus when we use a thin lens with a ocal length o 3.85-m?
8 Most Modern Telescopes Are Relectors Problems with reractors: Chromatic aberration: ocal length varies with wavelength Costly to make a large lens ree o deects, such as bubbles Light is absorbed and scattered in the glass Heavy to support, distortion under weight Advantages o relectors: The mirror is made to be highly relective. Fewer problems with chromatic aberration, glass deects, support and distortion. Spherical aberrations can be corrected. 1 " 1 = (n λ 1) 1 % $ ' λ # R 1 R 2 & nλ is the index o reraction at wavelength λ, Note that the index o reraction depends on wavelength (see R1 and R2 are the radii o curvature o the lens (negative radius or a diverging lens)
9 There are many designs o relecting telescopes, mostly with a primary mirror and a secondary mirror. Newtonian ocus Prime ocus Cassegrain ocus Coude ocus Gemini North Telescope on Mauna Kea
10 Newtonian Telescope Optics Most commonly used o the amateur telescopes Ease o construction, portability, insensitivity to alignment and cheap Primary mirror placed at the bottom o telescope tube Secondary mirror: small elliptically shaped lat mirror An alternative: Folded Newtonian provides high magniication with a long ocal length Main drawback: coma aberration at the edge o the ield o view A disadvantage is the extra obscuration caused by the circular lat
11 Cassegrain Telescope Optics Most commonly used o the astronomical night-time telescopes Longer eective ocal length and higher magniication Concave PM with a hole at its center: placed at the bottom o tube Convex SM with a small aperture: placed near the top o telescope Classical Cassegrain: a parabolic PM with a hyperbolic SM Dall-Kirkham system: an under-corrected parabolic PM with a spherical SM or direct viewing with small ield o view Ritchey-Chretien (RC) system: overcorrected hyperbolic PM and SM or a wide ield with a coma ree
12 Gregorian Telescope Optics Most commonly used o the solar telescopes Prime ocus or installation o solar heat stop Concave PM and SM: placed at the bottom and near the top o the telescope structure Concave SM with a small aperture: placed near the top o telescope Optics: a parabolic PM with a elliptical SM A disadvantage or on-axis Gregorian telescope is the extra obscuration caused by the SM and support structure
13 Nasmyth Telescope Optics A derivative o the Cassegrain and Gregorian telescopes Small lat mirror in ront o PM deliver the ocus to the side o telescope Nasmyth oci o very large astronomical telescopes provide access to proessional, bulky and heavy instrumentations 8 m Subaru Telescope
14 The world s largest telescopes are relectors.
15 The telescopes o Mauna Kea
16 Observatory on La Palma From let to right, the William Herschel Telescope, Dutch Open Telescope, the Carlsberg Meridian Telescope, the Swedish Solar Telescope, the Isaac Newton Telescope (second rom right) and the Jacobus Kapteyn Telescope (ar right) at Roque de los Muchachos. (Photo by Bob Tubbs)
17 European Southern Observatory (ESO) in Chile. (Copyright: R. Rekola)
18 6.2 Telescope Terms Clear Aperture Eective ocal length Focal ratio or -number Fast beam: small -number, short exposure time Slow beam: large -number, long exposure time The 1.6 m NST has an eective ocal length o 83.2 m, what is the -ratio at the Gregorian ocus? Image scale: 1 s = α (rad/mm) h = s" = ("/mm) 3438 s' = ('/mm) number = # = N = D
19 McMath-Piece Telescope has 1.52 m aperture, and ratio o Angular size o the Sun is about 32 (arc-minute), could you ind the physical size o the Sun on its ocal plane? s = α h = 1 (rad/mm) s" = ("/mm) s' = ('/mm) h = α e
20 6.3 Capabilities o Telescopes Magniication Power Light Gathering Power Resolving Power
21 Telescope Magniication Magniication is given by a ratio o the image size produced on the retina when looking through a telescope, versus retinal image size with the naked eye. Common eyepieces or telescopes are 26 mm and 12.5 mm. An /10 telescope o 8" aperture (203 mm) would provide corresponding magniications o 78X and 162X or these two eyepieces. ε tan ε ' e M T = = = = ' α tanα h / o h / o e D o M T = = = e d D d eye
22 Light Gathering Power Aperture diameter D: eective diameter o the telescope primary mirror. eye SDO/HMI Hinode NST ATST KECK 6mm 14cm 50cm 1.6m 4m 10m D π ( ) 2 d π ( ) = D 6 mm 2
23 The light gathering power o a telescope is proportional to the area o the objective lens/mirror, which is proportional to the square o the lens/mirror diameter - bigger telescopes produce brighter images. P = F obs A = Ex.1: The pupil size o the human eye is about 5mm, and its ocal length is 17mm. The largest reractor ever built has a diameter o 102 cm and ocal length o 19.5 m. (a) How many times greater is the light gathering power o this telescope compared to that o human eyes? (b) What s the magniication o the telescope i the ocal length o its eyepiece is the same as that o the human eye? 2 2 " 102 cm% " 1020 mm% (a) $ ' = $ ' = = # 5 mm & # 5 mm & (b) 19.5 m 17 mm L 4πd 2 π D2 4 = R2 σt 4 4d 2 πd 2 (J s -1 ) D 2 = mm 17 mm =
24 Telescope Resolution Rayleigh criterion: angle deined as that or which the central peak o one PSF alls upon the irst minimum o the other λ θ ( rad) = D λ ( µm) θ (") = 0.25 D ( m)
25 The angular resolution o a telescope is limited by diraction: bigger telescope, more details. Diraction limited angular resolution: θ = λ D θ = diraction limited angular resolution, in arcsec λ = wavelength o light, in meters D = diameter o telescope objective, in meters The angular resolution o a telescope determines how much detail we may see in an image -- the angular resolution o human eyes is 1 arcmin, and all planets have angular size o or less than 1 arcmin. Ex.2: Diraction limited angular resolution o Keck Telescopes (D = 10m): θ = 2.5x10 5 (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 10 5 (λ/θ) = 2.5x10 5 (0.03 m/1) = 7500 m (!)
26 Telescope Resolution Angular resolution: can be quantiied as the smallest angle between two point sources or which separate recognizable images are produced θ ( rad) = λ D 1 rad = " 1 " = 725 km on the Sun eye SDO/HMI Hinode NST ATST KECK 6mm 14cm 50cm 1.6m 4m 10m > km 534 km 150 km 47 km 19 km < 8 km
27 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 o larger objective ocal length to better resolve an image?
28 Key Words adaptive optics angular resolution baseline chromatic aberration chemical composition diraction ocal length ocal plane intererometry magniication objective lens objective mirror optical telescope radio telescope relecting telescope (relector) reracting telescope (reractor) seeing spectrograph spherical aberration
29 Reracting telescopes (reractors) orm images by bending light rays to a ocus point through glass lens. They have shortcomings like chromatic aberration, glass deects, and distortion by weight. Relecting telescopes (relectors) orm images by relecting light rays to the ocus rom curves mirrors, most used in modern astronomy. Theoretically, a telescope s diraction limited angular resolution depends on the diameter o the objective and observing wavelength. Summary Star trails above Mauna Kea (Peter Michaud, Gemini Observatory)
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