What is the approximate size of the smallest object on the Earth that astronauts can resolve by eye when they are orbiting 250 km above the Earth? Assume ? = 578 nm and a pupil diameter is 5.30 mm. (In this problem, you may use the Rayleigh criterion for the limiting angle of resolution of an eye.)

Pluto and its moon Charon are separated by 19600 km. An undergraduate researcher wants to determine if the 5.08 m diameter Mount Palomar telescope can resolve these bodies when they are 5.40×109 km from Earth (neglecting atmospheric effects). Assume an average wavelength of 545 nm. To determine the answer, calculate the ratio of the telescope's angular resolution ?T to the angular separation ?PC of the celestial bodies.

In June 1985, a laser beam was sent out from the Air Force Optical Station on Maui, Hawaii, and reflected back from the shuttle Discovery as it sped by, 354 km overhead. The diameter of the central maximum of the beam at the shuttle position was said to be 9.1 m, and the beam wavelength was 550 nm. What is the effective diameter of the laser aperture at the Maui ground station? (Hint: A laser beam spreads only because of diffraction; assume a circular exit aperture. A. 0.232 m B. 0.199 m c. 0.047 m D. 0.052 m

An amateur astronomer wants to build a telescope with a diffraction limit that will allow him to see if there are people on the moons of Jupiter.  (a) What diameter mirror is needed to be able to see 1.00 m detail on a Jovian Moon at a distance of 7.50×108 km from Earth? The wavelength of light averages 600 nm.  (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?