I Total focal length and magnification

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The discussion focuses on constructing a telephoto lens system to image a cantilever with dimensions of 450x50 microns, targeting a magnification between 4 and 8. It emphasizes that the image magnification is determined by the ratio of the focal lengths of two lenses, regardless of the total focal length. Questions arise about the relevance of total focal length when using different lens combinations that yield the same magnification, and whether the lensmaker's equation should be applied for calculating working distance. Additionally, there is a need for clarification on the setup, including the distances between the lenses and the sensor, and considerations for light collection and distortion in the imaging process. A detailed annotated diagram is suggested for better understanding and to facilitate more accurate responses.
Aymangh994
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I would like to realize an image of the cantilever. The dimensions are (450x50) microns. I would like to use a self-constructed telephoto lens. This consists of two lenses. The image magnification can be 4 to 8. The magnification of the image is nothing more than the ratio between the two focal lengths of the two lenses. E.g. for f1= 320mm f2=40mm the total f= 35.5mm and the imaging magnification is 8 . Since typical focal lenghts of telephoto are over 50mm, I would like to ask if the total focal length matters? I.e. for f1= 800mm and f2=100mm the total focal length is f=88.89 mm but the image magnification remains the same.
 
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You need to specify more about the set-up. What is "the cantilever"? We need an annotated diagram if you want sensible answers.
Edit: PS I think you are assuming the 'telescope formula' applies but your object distance is not infinite and are you looking at an image or projecting it onto a sensor?
 
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I would like to ask if the total focal length matters using two different combinations of lenses but the magnification still the same.
Combination 1 : f1= 320mm f2=40mm the total f= 35.5mm and M= 8
Combination 2 : f1= 800mm and f2=100mm the total focal length is f=88.89 mm and M= 8
and how to calculate the working distance ?
 
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following questions :
1. should I use the lensmaker's equation to calculate the working distance ? which focal length should I insert in the equation? the total f or f1 ?
2. The distance between the two lenses and the distance between the CCD-Sensor and the last lens ?
 

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You seem to be using a telescope rather than a microscope. In such a case, the objective lens should be as large as possible to collect maximum light, but may have to be stopped down to reduce distortion. The required magnification is very small - can this be obtained with a single lens?
 
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