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.)

What is bandwidth in an optical instrument? How does it relate to resolution and noise in an optical instrument?

Under ideal conditions and when Mars is closest, estimate the linear separation between two objects on Mars that can barely be resolved by (a) the naked eye and (b) the Hubble telescope (whose main mirror is 2.4 meters in diameter). (Hint: the answers are about 5000 km and 14 km)

Two 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.)

Suppose you want a telescope that would allow you to see distinguishing features as small as 6.5 km on the Moon some 384,000 km away. Assume an average wavelength of 550 nm for the light received. What is the minimum diameter of the mirror (in centimeters) that you could use in the telescope?

Suppose a microscope’s resolution is diffraction limited. Which one of the following changes would provide the greatest improvement to its resolution? (a) Observing at a longer wavelength through a smaller aperture. (b) Observing at a shorter wavelength through a larger aperture. (c) Decreasing the object distance. (d) Using a CCD sensor instead of a standard eyepiece.

These images show one of the large `VLT’ telescopes at the European Southern Observatory’s facility at Cerro Paranal, Chile. The place where the laser beam comes out (seen in the inset photo) is just out of sight off of the top edge of the large photo. Also note that if you look down the telescope tube (in the main photo), you can see the tube’s front-end structure. Imagine that this telescope had a flaw similar to the Hubble Space Telescope’s - its light-gathering element was shaped wrong. What problem would this cause for the telescope? Group of answer choices It would not be able to bring rays of light from a distant object to a focus. The imperfect shape would mean that it could focus rays of visible light, but not rays of light of any other wavelength. It wouldn’t be able to gather much light compared to the pupil of a human eye. It would mean that the telescope could only work if placed above the Earth’s atmosphere, like the Hubble telescope.

Spy planes fly at extremely high altitudes (25 km) to avoidinterception. If their cameras are to discern features assmall as 5 cm, what is the minimum aperture of the cameralens to afford this resolution? (Use λ=580nm )