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Resolution of a Telescope Each of the two telescopes at the Keck Observatory on the dormant Mauna Kea volcano in Hawaii has an effective diameter of 10 m. What is its limiting angle of resolution for 550 nm light? SOLUTION Conceptualize Identify the aperture through which the light travels as the opening of the telescope. Light passing through this aperture causes ---Select--- v patterns to occur in the final image. Categorize We determine the result using equations developed in this section, so we categorize this example as --Select--- v problem. Use this equation, taking 1 = 5.50 × 10-7 m and D = 10 m (Give your answer in rad.): O min = 1.22 D rad Any two stars that subtend an angle --Select--- or equal to this value are resolved (if atmospheric conditions are ideal). EXERCISE The Hale telescope on Mount Palomar has a diameter of 5.08 m (200 in.). Hint (a) If the smallest crater diameter the telescope can resolve on the Moon is 48.7 m, what wavelength light is being used? (Give your answer in nm. Assume the crater is 3.76 x 108 m from the telescope.) nm (b) What diameter crater (in m) could the Hubble telescope resolve using this wavelength, assuming the same distance as the Mount Palomar telescope. (The Hubble telescope's aperture diameter is 2.40 m.) (c) It appears that the Mount Palomar telescope has better resolution. Why is this misleading?

Resolution of a Telescope Each of the two telescopes at the Keck Observatory on the dormant Mauna Kea volcano in Hawaii has an effective diameter of 10 m. What is its limiting angle of resolution for 550 nm light? SOLUTION Conceptualize Identify the aperture through which the light travels as the opening of the telescope. Light passing through this aperture causes ---Select--- v patterns to occur in the final image. Categorize We determine the result using equations developed in this section, so we categorize this example as --Select--- v problem. Use this equation, taking 1 = 5.50 × 10-7 m and D = 10 m (Give your answer in rad.): O min = 1.22 D rad Any two stars that subtend an angle --Select--- or equal to this value are resolved (if atmospheric conditions are ideal). EXERCISE The Hale telescope on Mount Palomar has a diameter of 5.08 m (200 in.). Hint (a) If the smallest crater diameter the telescope can resolve on the Moon is 48.7 m, what wavelength light is being used? (Give your answer in nm. Assume the crater is 3.76 x 108 m from the telescope.) nm (b) What diameter crater (in m) could the Hubble telescope resolve using this wavelength, assuming the same distance as the Mount Palomar telescope. (The Hubble telescope's aperture diameter is 2.40 m.) (c) It appears that the Mount Palomar telescope has better resolution. Why is this misleading?

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Resolution of a Telescope Each of the two telescopes at the Keck Observatory on the dormant Mauna Kea volcano in Hawaii has an effective diameter of 10 m. What is its limiting angle of resolution for 550 nm light? SOLUTION Conceptualize Identify the aperture through which the light travels as the opening of the telescope. Light passing through this aperture causes ---Select--- v patterns to occur in the final image. Categorize We determine the result using equations developed in this section, so we categorize this example as --Select--- v problem. Use this equation, taking 1 = 5.50 × 10-7 m and D = 10 m (Give your answer in rad.): O min = 1.22 D rad Any two stars that subtend an angle --Select--- or equal to this value are resolved (if atmospheric conditions are ideal). EXERCISE The Hale telescope on Mount Palomar has a diameter of 5.08 m (200 in.). Hint (a) If the smallest crater diameter the telescope can resolve on the Moon is 48.7 m, what wavelength light is being used? (Give your answer in nm. Assume the crater is 3.76 x 108 m from the telescope.) nm (b) What diameter crater (in m) could the Hubble telescope resolve using this wavelength, assuming the same distance as the Mount Palomar telescope. (The Hubble telescope's aperture diameter is 2.40 m.) (c) It appears that the Mount Palomar telescope has better resolution. Why is this misleading?
Transcribed Image Text:Resolution of a Telescope Each of the two telescopes at the Keck Observatory on the dormant Mauna Kea volcano in Hawaii has an effective diameter of 10 m. What is its limiting angle of resolution for 550 nm light? SOLUTION Conceptualize Identify the aperture through which the light travels as the opening of the telescope. Light passing through this aperture causes ---Select--- v patterns to occur in the final image. Categorize We determine the result using equations developed in this section, so we categorize this example as --Select--- v problem. Use this equation, taking 1 = 5.50 × 10-7 m and D = 10 m (Give your answer in rad.): O min = 1.22 D rad Any two stars that subtend an angle --Select--- or equal to this value are resolved (if atmospheric conditions are ideal). EXERCISE The Hale telescope on Mount Palomar has a diameter of 5.08 m (200 in.). Hint (a) If the smallest crater diameter the telescope can resolve on the Moon is 48.7 m, what wavelength light is being used? (Give your answer in nm. Assume the crater is 3.76 x 108 m from the telescope.) nm (b) What diameter crater (in m) could the Hubble telescope resolve using this wavelength, assuming the same distance as the Mount Palomar telescope. (The Hubble telescope's aperture diameter is 2.40 m.) (c) It appears that the Mount Palomar telescope has better resolution. Why is this misleading?
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