Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Issues with the use of telescopesMagnificationMagnification determines how much larger the image is as compared to the size of the source of the light (the object)Magnification =fo fe Where fo is the focal length of the objective fe is the focal length of the eyepieceIssues with the use of telescopesMagnificationMagnification =fo fe A cheap telescope has an objective focal length of 600 mm, an objective diameter of 0.05 m and an eyepiece focal length of 20 mm. What is the magnification of this telescope?Given fo = 600 mm fe = 20 mmD = 0.05 mM = 600 mm / 20 mm = 30Issues with the use of telescopesMagnificationMagnification =fo fe A cheap telescope has an objective focal length of 600 mm , an objective diameter of 0.05 m and an eyepiece focal length of 5 mm. What is the magnification of this telescope?Given fo = 600 mm fe = 5 mmD = 0.05 mM = 600 mm / 5 mm = 120Issues with the use of telescopesMagnificationMagnification =fo fe An expensive telescope has an objective focal length of 2400 mm , an objective diameter of 0.2 m and an eyepiece focal length of 20 mm. What is the magnification of this telescope?Given fo = 2400 mm fe = 20 mmD = 0.2 mM = 2400 mm / 20 mm = 120Issues with the use of telescopesMagnificationQuestion: Is the cheap telescope with a 5 mm eyepiece as good as the expensive telescope with a 20 mm eyepiece?What do you think?Issues with the use of telescopesResolutionMore important (possibly more important) than magnification is resolution.Resolution – the property of an instrument to identify (resolve) small details.The smallest angular size identifiable by an instrument is given bymin = .25DWhere is the wavelength of the EM waves being collected in m (1 m = 10-6 m)D is the diameter of the aperture (the opening which collects the wave) in metersThe calculated value of will be in seconds of arc (arc seconds)Issues with the use of telescopesResolutionmin is called the diffraction limited resolution of the telescopeIssues with the use of telescopesResolutionFor the naked eye, Shortest visible wavelength 400 x 10-9 m = .4 m Diameter of the aperture (the pupil) 3 mm = 3 x 10-3 mθmin = (0.25) (0.4 ) / (3 x 10-3 ) ≈ 0.33 arc secmin 33” = .55’ = .0093o The average human eye can resolve object with an angular diameter of about a half a minute. min (in arc sec) = .25 (in m )D (in m)Issues with the use of telescopesResolutionFor the Mount Palomar 200 inch optical telescope, Shortest visible wavelength 400 x 10-9 m = .4 m Diameter of the aperture (the objective) = 200 in = 5.08 mθmin = (0.25) (0.4 ) / (5.08 ) ≈ 1.96 x 10-2 arc secmin 1.96 x 10-2 “ = 3.2 x 10-5 ‘ = 5.5 x 10-7 degreesThe Mount Palomar telescope can resolve objects about 1700 times smaller than the naked eye min (in arc sec) = .25 (in m )D (in m)Issues with the use of telescopesResolution – The Hubble Space TelescopeHubble works on the same principle as the first reflecting telescope built in the 1600s by Isaac Newton. Light enters the telescope and strikes a concave primary mirror, which acts like a lens to focus the light. The bigger the mirror, the better the image. In Hubble, light from the primary mirror is reflected to a smaller secondary mirror in front of the primary mirror, then back through a hole in the primary to instruments clustered behind the focal plane (where the image is in focus). Mirror sizePrimary mirror: 2.4 m – (94.5 inches) in diameterSecondary mirror: 0.3 m - (12 inches) in diameter Angular resolutionHubble's angular resolution is 0.05 arcsecond. This is the "sharpness" of Hubble's vision. If you could see as well as Hubble, you could stand in New York City and distinguish two fireflies, 1 m (3.3 feet) apart, in San Francisco.Issues with the use of telescopesResolutionIf the Mount Palomar 200 inch optical telescope recorded radio waves of wavelength 1 meter, wavelength 1 m = 1 x 106 m Diameter of the aperture (the objective) = 200 in = 5.08 mθmin = (0.25) (0.1 x 106 ) / (5.08) ≈ 4.9 x 104 arc secmin 4.9 x 104 “ = 820’ = 13.7o The angular diameter of the moon = 30’ The angular diameter of the Andromeda Galaxy 178’The Mount Palomar telescope would not be able to resolve these objectsIt would not be able to “see” the moon ! min (in arc sec) = .25 (in m )D (in m)Issues with the use of telescopesResolutionFor the National Radio Astronomical Observatory Robert C. Byrd Radio Telescope, wavelength 1 m = 1 x 106 m Diameter of the aperture (the objective) = 100 mθmin = (0.25) (1 x 106 ) / (100 ) ≈ 2500 arc secmin 2500” = 41’ = .69o The angular diameter of the moon = 30’ The angular diameter of the Andromeda Galaxy 178’The NRAO telescope would be able (roughly) to resolve radio sources of these angular diametersmin (in arc sec) = .25 (in m )D (in m)Issues with the use of telescopesResolutionFor the Arecibo Radio telescope, wavelength 1 x 106 m Diameter of the aperture (the objective) = 305 mθmin = (0.25) (1 x 106 ) / (305 ) ≈ 819 arc secmin 819” = 13.7’ = .22o The angular diameter of the moon = 30’ The angular diameter of the Andromeda Galaxy 178’The Arecibo telescope would easily be able to resolve radio sources of these angular diametersmin (in arc sec) = .25 (in m )D (in m)Issues with the use of telescopesMagnificationQuestion: Is the cheap telescope with a 5 mm eyepiece as good as the expensive telescope with a 20 mm eyepiece?The magnifications in both cases are the same. However, the diffraction limited resolutions are (using 0.4 μm for the visible wavelength)Θmin,cheap = (0.25) (0.4) / (0.05) = 2 arc secΘmin,expensive = (0.25) (0.4) / (0.2) = 0.5 arc secThe expensive telescope will resolve objects 4 times smaller than the cheap telescope. In part, the expense of a larger telescope is related to resolution more that
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