Optics Tutorial 4 HW solutions

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?

 
No equations here! For unity mag, the image distance has to equal the object distance. By inspection one can tell the load line will always be at a 45° and therefore the focal length is half the object distance or F = 21.85 mm and the image distance is equal to the object distance or o = 43.7 mm

In my circuit classes I hated to hear "by inspection", but now I'm using it:)

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?


This last solution shows how the nomograph can be used and also confuse the sign conventions. The figures at left used to set up the equations via similar triangles are actually wrong. I didn't realize that until I got a negative solution... which told me that the nomograph was wrong. The correct one is shown in the lower right. I could have redone the problem starting with the "correct" nomograph and I would have gotten a positive answer. I chose to keep this to show it's use.


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Scott Sparrold,
Mar 7, 2013, 8:26 AM
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Scott Sparrold,
Mar 7, 2013, 8:44 AM
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Scott Sparrold,
Mar 7, 2013, 8:47 AM
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Scott Sparrold,
Mar 7, 2013, 8:57 AM
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