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Tutorial 4 - Imaging Nomograph

By Scott Sparrold

If you are like me, then you crave a deep understanding of how optics works. This nomograph beautifully shows how the lens makers equation works, by giving a cartesian coordinate system for the conjugates and another axis for the focal length. A load line shows their interactions.

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  1. The total track, or the object to image distance, is 139 mm. What is the focal length required to have a 2x magnification? Where is the lens located relative to the object? (Magnification hint: the image distance is twice the object distance)
  2. A virtual object is 30 mm inside a negative lens of focal length -100 mm. Where is the image?
  3. Your new boss tells you to go into a lab and “focus a lens” for unity magnification. Upon entering there is an optical rail with three components: An illuminated pinhole, a lens and a camera. After moving this stuff around to get mag = 1.0, you find the pinhole is 43.7 mm from the lens. What is the focal length of the lens? What is the distance from the lens to the camera?
  4. Upon completing problem #3 above your new boss comes in and shows you that you lens is a liquid lens that is capable of changing focal lengths (opto-tune Edmund Optics part # 83918. He changes the focal length to what he claims is 80 mm. After refocusing the camera, what is the lens to camera distance?
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Solutions found here.