Compare the angular resolving power of the following imaging instruments (details of the italicized instruments are to be covered later). Take the wavelength of light as 5 x 10-7m. (a) the eye with an effective aperture of 0.5 cm (b) a pair of binoculars using a typical aperture of the front lenses (c) the Yerkes Observatory optical telescope, with a diameter of roughly 1.0 m (d) the Manchester radiotelescope, with a diameter of 76.2 m, using microwave radiation of wavelength 22 cm
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- The minimum angular separation -6 between two stars is 4 x 10° rad, if telescope is used to observe them with an objective of aperture 16 cm. Find the wavelength of light used.A space-based telescope can achieve a diffraction-limitedangular resolution of 0.05" for red light (wavelength 700 nm). What would the resolution of the instrument be in the ultraviolet, at wavelength 140 nm?The telescope and CCD detector described in question 2 are used to observe a distant star cluster. The detector has 2000 x 2000 pixels. What is the minimum angular separation between two stars in the cluster that can just be resolved with this observing system if we ignore the effects of diffraction and the Earth's atmosphere? Assume the two stars are resolved if they are able to fall on the centres of two neighbouring pixels. Choose the answer below that best matches your answer. Select one: Оа. 2.5" O b. 0.07" O C. 0.15" d. 1.3" е. 0.80"
- Suppose a 5.00 m diameter telescope were constructed on the Moon, where the absence of atmospheric distortion would permit excellent viewing. If observations were made using 500 nm light, what minimum separation between two objects could just be resolved on Mars at closest approach (when Mars is 8.0 × 107 km from the Moon)?A certain telescope has a 10' × 10' field of view that is re- corded using a CCD chip having 2048 x 2048 pixels. What angle on the sky corresponds to 1 pixel? What would be the di- ameter of a typical seeing disk (1" radius), in pixels?A camera has a lens diameter of 0.0444 m. What wavelength of light IN NANOMETERS must it use to resolve two objects 550 m away that are 0.00718 m apart? [?] nm Hints: Solve for A! The answer should be between 400 and 700. Remember, nano means 10-9.
- What is bandwidth in an optical instrument? How does it relate to resolution and noise in an optical instrument?Consider a telescope on Earth that aims to distinguish (solve) two points over the moon separated by a distance of 1.7 km when the moon is at a distance of 3.8x105 km. By the Rayleigh resolution criterion, what is the minimum diameter of the opening of this telescope? Consider the wavelength equal to 0.55 µm. 21 cm 12 cm 25 cm 15 cm 18 cmYou use a lens of diameter D and light of wavelength l and frequency f to form an image of two closely spaced and distant objects. Which of the following will increase the resolving power? (a) Use a lens with a smaller diameter; (b) use light of higher frequency; (c) use light of longer wavelength. In each case justify your answer.
- Find the separation of two points on the Moon’s surface that can just be resolved by the 200 in. (= 5.1 m) telescope at Mount Palomar, assuming that this separation is determined by diffraction effects. The distance from Earth to the Moon is 3.8* 10^5 km.Assume a wavelength of 550 nm for the lightTwo stars are separated by 1 x 10" m and are 4 light years away. Calculate the resolving power of the Hubble Space Telescope, with a diameter of 2.4m, at this distance. Can the Hubble Space Telescope resolve the two stars? Assume the wavelength of light is 650nm. (Hint: Look up the conversion of light years to meters.)The Hubble Space Telescope has an aperture of 2.4m and focuses visible light (380–750 nm). The Arecibo radio telescope in Puerto Rico is 305m in diameter (it is built in a mountain valley) and focuses radio waves of wavelength 75 cm. (a) Under optimal viewing conditions, what is the diameter of the smallest possible crater that each of these telescopes could resolve on our moon?