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Robert Clark
member
Reged: 01/09/05
Posts: 16
Loc: Philadelphia, PA.
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Re: Optical high data rate space transmissions.
07/06/09 11:00 AM
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O.K. I found this page with the equation for concave mirrors:
The Mirror Equation - Concave Mirrors.
http://www.glenbrook.k12.il.us/gbssci/phys/class/refln/u13l3f.html
The mirror equation gives the relationship between the focal length, the object distance, and the image distance:
1/f = 1/do + 1/di
The object and image distances determine the magnification, which is the ratio of the image size to object size:
M = hi/ho = - di/do, where the minus sign indicates the image would be inverted.
The object distance is the distance to the Sun at about 150,000,000 km. The image distance would be the distance from the Moon to the Earth at 380,000 km. Because the solar distance is so much larger than the lunar distance, the Earth would be quite close to the focus.
The size of the image is obtained from the equation hi/ho = - di/do, hi/1,400,000 = - 380,000/150,000,000, using 1,400,000 km for the size of the Sun. So hi = -3,547 km, with an inverted image.
What I'm still puzzling about, assuming the idea that a 4 m mirror at lunar distance would have an apparent magnitude of +3 is correct, is would this mean all the observers in that 3,547 km wide area would view it as being of +3 magnitude?
Bob Clark
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