Explanation Given info: The given diffraction arrangements are (i) a radio telescope 100 m in diameter observing at a wavelength of 21 cm ; (ii) an optical telescope 2.0 m in diameter observing at a wavelength 500 nm ; (iii) an ultraviolet telescope 1.0 m diameter observing at a wavelength of 100 nm ; (iv) an infrared telescope 2.0 m in diameter observing at a wavelength of 10 μm . Write the expression for the diffraction angle by a circular aperture. sin θ 1 = 1.22 λ D Here, θ 1 is the angular radius of the first maximum λ is the wavelength of light D is the diameter of the aperture Combining this expression with the Rayleigh’s criterion for resolution shows that, the resolving power of a telescope increases as the ratio λ / D decreases. Determining the value of λ / D and arranging them in order of lowest to highest gives the order of ability of the telescopes to resolve small details, from best to worst. Substitute 100 nm for λ and 21 cm for D to find the value of λ / D for the telescope (i). λ D = 21 cm 100 m = 21 cm × 10 − 2 m 1 m 100 m = 2.1 × 10 − 3 Substitute 500 nm for λ and 2.0 m for D to find the value of λ / D for the telescope (ii). λ D = 500 nm 2

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

14th Edition

ISBN: 9780134265414

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Chapter 36.7, Problem 36.7TYU

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To arrange: The given proposed telescopes in order of their ability to resolve small details, from best to worst.

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Chapter 36.6, Problem 36.6TYU

Chapter 36, Problem 36.1DQ

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You have been asked to compare four proposals for telescopes to be placed in orbit above the blurring effects of the earth’s atmosphere. Rank the proposed telescopes in order of their ability to resolve small details, from best to worst. (i) A radio telescope 100 m in diameter observing at a wavelength of 21 cm; (ii) an optical telescope 2.0 m in diameter observing at a wavelength of 500 nm; (iii) an ultraviolet telescope 1.0 m in diameter observing at a wavelength of 100 nm; (iv) an infrared telescope 2.0 m in diameter observing at a wavelength of 10 mm.

What is the resolving power of a 25-cm (10-in.) telescope at a wavelength of 550 nm (in the middle of the visual band)?

In the dark, your pupil (the aperture of your eye) expands to a diameter of 7 mm. How many times more light can be gathered by a telescope with a 5.5 m diameter than by a fully dark- adapted eye? Increase in light gathered = I times

Chapter 36 Solutions

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

Ch. 36.1 - Can sound waves undergo diffraction around an...Ch. 36.2 - Rank the following single-slit diffraction...Ch. 36.3 - Coherent electromagnetic radiation is sent through...Ch. 36.4 - Suppose two slits, each of width a, are separated...Ch. 36.5 - What minimum number of slits would be required in...Ch. 36.6 - Prob. 36.6TYU Ch. 36.7 - Prob. 36.7TYU Ch. 36 - Why can we readily observe diffraction effects for...Ch. 36 - Prob. 36.2DQ Ch. 36 - You use a lens of diameter D and light of...

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The given proposed telescopes in order of their ability to resolve small details, from best to worst.

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To arrange: The given proposed telescopes in order of their ability to resolve small details, from best to worst.

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Chapter 36 Solutions