EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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Textbook Question
Chapter 35, Problem 23P
(I) What is the angular resolution limit (degrees) set by diffraction for the 100-inch (254-cm mirror diameter) Mt. Wilson telescope (λ = 560nm)?
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(i.) What must be true in order for two objects to be resolvable? (ii.) Suppose a 5.0 m diameter telescope were constructed on the far side of the Moon. To prove that the viewing there would be excellent, what would be the separation between two objects that could just be resolved on Mars in 500. nm light? [Use the Mars-Moon distance of 80.5 million km.] Show all work and answer both parts of the question.
Question 1
a)Calculate the resolving power of a Fabry-Perot interferometer made of re-
flecting surfaces of reflectivity 0.85 and separated by a distance 1 mm at
λ = 4880 ˚A.
b. Calculate the minimum spacing between the plates of a Fabry?Perot interfer-
ometer which will resolve two lines with ∆λ = 0.1 ˚Aat λ = 6000 ˚A. Assume
the reflectivity to be 0.8.
need both or else I will downvote
in the question: A spy satellite orbiting 600 km above Earth is supposedly capable of counting individual people in a crowd in visual- wavelength images. Assume that the middle of the visual wavelength band is at 550 nm . Assume an average person has a size of 0.8 m as seen from above. Estimate the minimum telescope diameter that the satellite must carry.
The previous expert used 1,22 instead of 2.06 to convert to angular distance. I thinkn he has to use the small-angular formula.
Chapter 35 Solutions
EBK PHYSICS FOR SCIENTISTS & ENGINEERS
Ch. 35 - Radio waves and light are both electromagnetic...Ch. 35 - Hold one hand close to your eye and focus on a...Ch. 35 - Explain why diffraction patterns are more...Ch. 35 - For diffraction by a single slit, what is the...Ch. 35 - Describe the single-slit diffraction pattern...Ch. 35 - What happens to the diffraction pattern of a...Ch. 35 - In the single-slit diffraction pattern, why does...Ch. 35 - Discuss the similarities, and differences, of...Ch. 35 - Figure 3510 shows a two-slit interference pattern...Ch. 35 - When both diffraction and interference are taken...
Ch. 35 - Does diffraction limit the resolution of images...Ch. 35 - Give at least two advantages for the use of large...Ch. 35 - Atoms have diameters of about 108 cm. Can visible...Ch. 35 - Which color of visible light would give the best...Ch. 35 - Could a diffraction grating just as well be called...Ch. 35 - Suppose light consisting of wavelengths between...Ch. 35 - What is the difference in the interference...Ch. 35 - White light strikes (a) a diffraction grating and...Ch. 35 - (I) If 680-nm light falls on a slit 0.0365 mm...Ch. 35 - (II) (a) For a given wavelength , what is the...Ch. 35 - (II) If you double the width of a single slit, the...Ch. 35 - (II) If a double-slit pattern contains exactly...Ch. 35 - (II) Design a double-slit apparatus so that the...Ch. 35 - (II) Suppose d = D in a double-slit apparatus, so...Ch. 35 - (II) In a double-slit experiment, let d = 5.00D =...Ch. 35 - (I) What is the angular resolution limit (degrees)...Ch. 35 - (II) The nearest neighboring star to the Sun is...Ch. 35 - (II) The normal lens on a 35-mm camera has a focal...Ch. 35 - (I) A source produces first-order lines when...Ch. 35 - (II) A tungstenhalogen bulb emits a continuous...Ch. 35 - (II) Show that the second- and third-order spectra...Ch. 35 - (II) Suppose the angles measured in Problem 40...Ch. 35 - (II) Missing orders occur for a diffraction...Ch. 35 - The Hubble Space Telescope with an objective...
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- Assuming the angular resolution found for the Hubble Telescope in Example 4.6, what is the smallest detail that could be observed on the moon?arrow_forwardA light ray of wavelength 461.9 nm emerges from a 2-mm circular aperture of a krypton ion laser. Due to diffraction, the beam expands as it moves out. How large is the central bright spot at (a) 1 m, (b) 1 km, (c) 1000 km, and (d) at the surface of the moon at a distance of 400,000 km from Earth.arrow_forwardHow far apart must two objects be on the moon to be resolvable by the 8.1-m-diameter Gemini North telescope at Mauna Kea, Hawaii, if only the diffraction effects of the telescope aperture limit the resolution? Assume 550 nm for the wavelength of light and 400,000 km for the distance to the moon.arrow_forward
- A telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The laser beam is sent through the telescope in opposite the normal direction and can then be projected onto a satellite or the moon. (a) If this is done with the Mount Wilson telescope, producing a 2.54-m-diameter beam of 633-nm light, what is the minimum angular spread of the beam? (b) Neglecting atmospheric effects, what is the size of the spot this beam would make on the moon, assuming a lunar distance of 3.84108 m?arrow_forwardOn a certain crystal, a first-order X-ray diffraction maximum is observed at an angle of 27.1° relative to its surface, using an X-ray source of unknown wavelength. Additionally, when illuminated with a different, this time of known wavelength 0.137 nm, a second-order maximum is detected at 37.3°. Determine (a) the spacing between the reflecting planes, and (b) the unknown wavelength.arrow_forwardWhat is the minimum diameter mirror on a telescope that would allow you to see details as small as 5.00 km on the moon some 384,000 km away? Assume an average wavelength of 550 nm for the light received.arrow_forward
- A camera uses a lens with aperture 2.0 cm. What is the angular resolution of a photograph taken at 700 nm wavelength? Can it resolve the millimeter markings of a ruler placed 35 m away?arrow_forwardThe angular resolution of a radio telescope is to be 0.100 when the incident waves have a wavelength of 3.00 mm. What minimum diameter is required for the telescopes receiving dish?arrow_forwardHow far apart must two objects be on the moon to be distinguishable by eye if only the diffraction effects of the eye’s pupil limit the resolution? Assume 550 nm for the wavelength of light, the pupil diameter 5.0 mm, and 400,000 km for the distance to the moon.arrow_forward
- Check Your Understanding What is the angular resolution of the Arecibo telescope shown in Figure 4.20 when operated at 21-cm wavelength? How does it compare to the resolution of the Hubble Telescope? Figure 4.20 A 305-m-diameter paraboloid at Arecibo in Puerto Rico is lined with reflective material, making it into a radio telescope. It is the largest curved focusing dish in the world. Although D for Arecibo is much larger than for the Hubble Telescope, it detects radiation of a much longer wavelength and its diffraction limit is significantly poorer than Hubble’s. The Arecibo telescope is still very useful, because important information is carried by radio waves that is not carried by visible light. (credit: Jeff Hitchcock)arrow_forward(a) What is the angular separation of two stars if their images are barely resolved by the Thaw refracting telescope at the Allegheny Observatory in Pittsburgh? The lens diameter is 76 cm and its focal length is 14 m. Assume l = 550 nm. (b) Find the distance between these barely resolved stars if each of them is 10 light-years distant from Earth. (c) For the image of a single star in this telescope, find the diameter of the first dark ring in the diffraction pattern, as measured on a photographic plate placed at the focal plane of the telescope lens. Assume that the structure of the image is associated entirely with diffraction at the lens aperture and not with lens “errors.”arrow_forwardCalculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star.. (a) 610 x 10⁹ rad -9 (b) 305 x 10⁹ rad ma (c) 457.5 x 109 rad (d) 152.5 x 10⁹ radarrow_forward
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