Optics question

  • Thread starter Vanush
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  • #1
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If I have a camera orbiting in space way above the Earth, and it has a diffraction limited resolution of 4.1*10^-7 m (diameter of airy disc), then how can I find out the corresponding value if the lens is supposed to take images of the Earth?
 

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  • #2
mgb_phys
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What do you mean by "corresponding value"?
Presumably by the 4.1*10^-7 m you mean the resolution limit at the image plane.
If you knowthe focal length and orbital height you can work out the resolutionsize on the earth's surface
 
  • #3
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What do you mean by "corresponding value"?
Presumably by the 4.1*10^-7 m you mean the resolution limit at the image plane.
If you knowthe focal length and orbital height you can work out the resolutionsize on the earth's surface

Yeah, how do I figure out the res on the Earth? I know the Focal length and orbital height. I was thinking you could just multiply the airy disk size by 100000 for 100km
 
  • #4
Redbelly98
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Note that multiplying (airy disc diameter) x (orbital height) gives incorrect units of m^2, when we're looking for an answer in meters.

Hint: what is the camera's magnification factor?
 
  • #5
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So I'm looking for a dimensionless number? Not sure what it could be, i'm only given lens diamater, focal length and wavelength.
 
  • #6
Redbelly98
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Resolution at the Earth's surface will have units of meters.

Eg.: the camera can distinguish objects on Earth that are ___ meters apart.
 
  • #7
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yeah, I'm having trouble figuring out how I can get that very small airy disc size to correspond to resolution on the Earth's surface, 100km's away. I tried using this
ea350ccdc729cf3d0385636f2115ce35.png

where di is distance to the image from the lens, and do is distance to the object. But, then I get a very small number and if i multiply this number with the airy disc size I don't get a realistic resolution on the Earth's surface.
 
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  • #8
Redbelly98
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Which of these seems more reasonable to you:

(object) x (magnification) = (image)
or
(image) x (magnification) = (object)

?
 
  • #9
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Which of these seems more reasonable to you:

(object) x (magnification) = (image)
or
(image) x (magnification) = (object)

?

First one.
 
  • #10
Redbelly98
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Good.

Does the 4.1*10^-7 m Airy disk correspond to an object or image?
 
  • #11
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Good.

Does the 4.1*10^-7 m Airy disk correspond to an object or image?

image
 
  • #12
Redbelly98
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Sounds like you can use the 1st equation in post #8 to solve the problem now.
 

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