## Problems

5.3 Image formation

Problem 5.31. (a) Confirm that the Lick 3-m telescope has plate scale of ~ 14"/mm, given its focal length of 15.2 m. What distance on the plate would correspond to a great circle angle of 1°? (b) What is the focal ratio R of this telescope? (c) A detectable image of a distant star (i.e., a point source) can be obtained on film at the focus of the telescope in an exposure of duration T if the flux density (W m-2) at the telescope is The circular image size is 1" in radius due to variable atmospheric refraction. How long does it take to detect a uniformly bright nebula of angular radius 2' if its total flux is 1000^ ? (d) What would be the required exposure time if the telescope were 1/4 the size of the Lick 3-m in all respects, i.e., d = 0.75 m and fL = 3.8 m? [Ans. -0.2 m; -5; -15T; —]

### 5.4 Antenna beams

Problem 5.41. Why is it desirable to have ground-based optical telescopes larger than the 0.40-m aperture which provides the best-possible resolution for a traditional telescope?

Problem 5.42. (a) What is the diffraction-limited resolution in arcsec of the Arecibo radio telescope "dish" of diameter 300 m operating at a wavelength of 20 mm? (b) If instead one had two such telescopes separated from one another by 10 km, what resolution (arcsec) might be attained, at the same wavelength? Repeat if the telescopes are separated by 7500 km (e.g., on different continents). (c) What is the theoretical diffraction-limited resolution for a 1-m diameter x-ray telescope for 1 keV photons (in arcsec)? [Ans. ~15''; ~0.5'', —10-3''; ~10-3'5'']

### 5.5 Resolution enhancement

Problem 5.51. Describe the nature of the speckle pattern as a function of time that one might expect from a large telescope (e.g., 2.4-m diameter) and compare this to that expected for a small telescope of diameter only 50 mm. In each case, how many speckles might be expected and how might they appear to move according to an observer watching the pattern through an eyepiece? The turbulent cells in the atmosphere are typically 0.1 m in diameter.

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