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I have been given this problem in my first week of classes in Physics:
The McMath-Pierce Solar Telescope at Kitt Peak National Observatory in Arizona is a reflecting telescope (i.e., a concave mirror) of diameter 1.61 m and a focal length of 87.0 m. There is a screen in the focal plane of the mirror, so the image of the Sun can be viewed. Assume for this problem that there are no other mirrors, and the screen and image are located at the actual focal plane of the mirror. (In reality, two other mirrors are used to reflect the image to a fixed location in an observing room.)
a. The angular diameter of the Sun in our sky is 0.535 degree. (This is the angle taken up by the diameter of the Sun, as seen from the Earth.) What is the diameter of the image of the Sun, in metres? Drawing a diagram of the situation might be helpful.
b. At a time when the telescope is pointing at a blank patch of sky (not at the Sun), a Red-tailed Hawk glides towards the west across the optic axis of the telescope at a distance of 410 m from the mirror. The hawk is 56.0 cm in length (beak to tail), and is moving perpendicularly to the optic axis at a speed of 3.60 m/s.
How far from the mirror would the hawk's image form if the screen weren't there (so that the image actually could form)?
How long would the image be (beak to tail)?
What would be the speed of the image, in m/s?
iv. In what direction would the image be traveling?
v. Since the screen prevents the image from forming, what does an astronomer watching the screen really see? (e.g., nothing? a sharp-edged shape bigger than the image? a blur? or…?)
I can't figure out how to do this, can somebody help?
Thanks
The McMath-Pierce Solar Telescope at Kitt Peak National Observatory in Arizona is a reflecting telescope (i.e., a concave mirror) of diameter 1.61 m and a focal length of 87.0 m. There is a screen in the focal plane of the mirror, so the image of the Sun can be viewed. Assume for this problem that there are no other mirrors, and the screen and image are located at the actual focal plane of the mirror. (In reality, two other mirrors are used to reflect the image to a fixed location in an observing room.)
a. The angular diameter of the Sun in our sky is 0.535 degree. (This is the angle taken up by the diameter of the Sun, as seen from the Earth.) What is the diameter of the image of the Sun, in metres? Drawing a diagram of the situation might be helpful.
b. At a time when the telescope is pointing at a blank patch of sky (not at the Sun), a Red-tailed Hawk glides towards the west across the optic axis of the telescope at a distance of 410 m from the mirror. The hawk is 56.0 cm in length (beak to tail), and is moving perpendicularly to the optic axis at a speed of 3.60 m/s.
How far from the mirror would the hawk's image form if the screen weren't there (so that the image actually could form)?
How long would the image be (beak to tail)?
What would be the speed of the image, in m/s?
iv. In what direction would the image be traveling?
v. Since the screen prevents the image from forming, what does an astronomer watching the screen really see? (e.g., nothing? a sharp-edged shape bigger than the image? a blur? or…?)
I can't figure out how to do this, can somebody help?
Thanks