6. Two stars are 5.1 x 101 m apart and are equally distant from the earth. A telescope has an objective lens with a diameter of 1.51 m and just detects these stars as separate objects. Assume that light of wavelength 550 nm is being observed. Also, assume that diffraction effects, rather than atmospheric turbulence, limit the resolving power of the telescope. Find the maximum distance that these stars could be from the earth.
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- 1. A single-colour source reaches 1st to 9th slit with a distance of 7.7 centimeters. The screen is 9 meters away from the slits. The slit separation is 743 µmeters. Calculate the wavelength of the light.1. Two coherent radio point sources separated by 2.0m are radiating in phase with a wavelength 1-0.50m. A detector moved in a circular path around the two sources in a plane containing them will show how many maxima?The width of a telescope aperture is important because it determines what you will be able to resolve. (a) You are out stargazing with your 11.2-cm telescope. You point your telescope at an interesting formation in the sky, which you think is a binary star system. A binary star system consists of two stars in orbit around each other. You guess that the average wavelength coming from the stars is 526 nm. What is the minimum angular separation between the two stars required for your telescope to resolve the two stars of the binary system? rad (b) Having graduated with a degree in astronomy, you seek a job at the Arecibo radio telescope. You use a large radio telescope (300-m diameter) to observe the same binary system that you observed in part (a). You estimate that the average radio emissions from the system have a wavelength of 5.04 cm. What is the minimum angular separation required for the Arecibo telescope to resolve the two stars of the binary system? rad Additional Materials
- Diffraction due to a circular aperture is important in astronomy. Since a telescope has a circular aperture of finite size, stars are not imaged as points, but rather as diffraction patterns. Two distinct points are said to be just resolved (i.e., have the smallest separation for which you can confidently tell that there are two points instead of just one) when the center of one point's diffraction pattern is found in the first dark ring of the other point's diffraction pattern. This is called Rayleigh's criterion for resolvability. Consider a telescope with an aperture of diameter 1.02 m. Part D What is the angular radius 0₁ of the first dark ring for a point source being imaged by this telescope? Use 550 nanometers for the wavelength, since this is near the average for visible light. Express your answer in degrees, to three significant figures. xa — ΑΣΦ Xb 0₁ 5.39 10 = 7 √x x x <४ |X| Submit Previous Answers Request Answer ? X.10n X You have already submitted this answer. Enter a new…7. A spy camera is said to be able to read the numbers on a car's license plate. If the numbers on the plate are 3.70 cm apart, and the spy satellite is at an altitude of 200 km, what must be the diameter of the camera's aperture? (Assume light with a wavelength of 600 nm.) m,5. A diffraction-limited telescope with a 7.6 cm aperture is aimed at target 12.5 km away. Assuming light of 580 nm wavelength and neglecting air turbulence, what size details can be resolved by the telescope? A) 8.2 cm B) 10.0 cm C) 11.3 cm D) 12.43 cm E) 12.88 cm
- 5. The Hubble Space Telescope with an objective diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light with wavelength 550 nm. Assume that the Hubble is near the Earth.4. Pluto and its moon Nix are separated by 48700 km. An undergraduate researcher wants to determine if the 5.08 m diameter Mount Palomar telescope can resolve the bodies when they are 6.40x109 km from Earth. Assume an average wavelength of 535 nm for the light. To determine the answer, calculate the ratio of the telescope’s angular resolution θT to the angular separation θP N of the celestial bodies.39. Astronomers have discovered a planetary system orbiting the star Upsilon Andromedae, which is at a distance of 4.2 × 10¹7 m from the earth. One planet is believed to be located at a distance of 1.2 × 10¹¹1 m from the star. Using visible light with a vacuum wavelength of 550 nm, what is the minimum necessary aperture diameter that a telescope must have so that it can resolve the planet and the star?
- . The glass lens is coated with a thin film with a thickness of 340 nm and a refractive index of 1.48. Determine the wavelengths of the visible region that are missing from the reflected light when the refractive index of the glass is a) 1.39 b) 1.69.Two stars are 2.5 × 1011 m apart and are equally distant from the earth. A telescope has an objective lens with a diameter of 1.98 m and just detects these stars as separate objects. Assume that light of wavelength 540 nm is being observed. Also, assume that diffraction effects, rather than atmospheric turbulence, limit the resolving power of the telescope. Find the maximum distance that these stars could be from the earth.13. Suppose that you have a laser of wavelength 2 = 450 nm, and a single slit with a width of a = 0.16 mm. You plan to place the slit exactly L = 1.00 m away from a viewing screen, but you want to predict the positions of the dark fringes in advance. First, let's check if the small-angle approximation applies to this situation. a. Use på a sin 0 to calculate the angle 8₁ for the first order (p = 1) dark fringes: = b. Calculate sin 0₁: c. Calculate tan 0₁: d. Compare the values for sin 0, and tan 8₁. Are these approximately equal? If so, then we can use the small angle approximation 0, (rad) ≈ P²P for further R a L calculations, and the dark fringes should be equally spaced. S 2015 #10772/ 754911 My PORTALLA 1500 ALTERNA