Design a telescope and the light gathering power of the telescope.

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Chapter 6, Problem 14P

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Design a telescope and the light gathering power of the telescope.

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Astronauts observing from a space station need a telescope with a resolving power of 0.6 arc second at a wavelength of 530 nm and a magnifying power of 220. Design a telescope to meet their needs.What will its light-gathering power be, compared with a dark-adapted human eye? (Assume that the pupil of your eye can open to a diameter of about 0.8 cm in dark conditions.)(State the necessary primary diameter of the telescope, in m, and the ratio of the focal lengths below.)

Astronauts observing from a space station need a telescope with a resolving power of 0.9 arc seconds at a wavelength of 540 nm and a magnifying power of 260. Design a telescope to meet their needs. (State the necessary primary diameter of the telescope, in m, and the ratio of the focal lengths below. Also, what will its light-gathering power be, compared with a dark adapted human eye? (Assume that the pupil of your eye can open to a diameter of about 0.8 cm in dark conditions.)

spy satellite orbiting 410 km above Earth is supposedly capable of counting individual people in a crowd in visual-wavelength images. Assume that the satellite's cameras operate at a wavelength of 550 nm. Assume an average person has a size of 0.6 m as seen from above. Estimate the minimum telescope diameter that the satellite must carry. (Hint: Use The small-angle formula angular diameter (arc seconds) 2.06 105 = linear diameter distance to convert linear size to angular size.)