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Find the position of the lens

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In the given optical instrument in which manner third lens of same focal length can be inserted in order to increase the collecting efficiency of light without changing the position of object and image. calculate the position of that lens
I am unable to understant collecting efficiency I tried to search it on Internet but still didn't get much help , then how should I proceed ?

asked Jan 30, 2017 in Physics Problems by physicsapproval (2,320 points)
Collecting efficiency is related to throughput. See for example this tutorial : https://www.newport.com/t/light-collection-and-systems-throughput. The idea is to look at marginal rays. Try drawing some ray diagrams to get a feel for the problem.

The question says that the object and image remain in the same position, but it does not say that the magnification is the same. The new image could be inverted. Neither does the question state that the first 2 lenses must remain in their current positions - so perhaps these could be moved?
I still don't get you  I think we should keep the original lenses untouched then furter how can I use collecting efficiency here in  the question?
Yes I agree. The question only asks for the position of the new lens, so probably the lenses in the diagram should not be moved.

Sorry I don't know what the answer is, but I will think about it some more. Meanwhile, as I suggested, you could draw some diagrams to get a feel for the problem. You need to examine what happens to the marginal rays.
https://cdn.pbrd.co/images/szf2zrcfj.gif

According to the figure on the site provided by you I think as in the Middle (2nd) lens  it is kept very near to object near to object within its focal range and actually it matches with the answer wich say "anything less than 10cm to the right of object"
But then I don't know whether this is to be calculated qualitatively or can it be mathematically proved?
That answer does not see right. If the position of the 3rd lens changes ("anything less than 10cm...") then the position of the image will change. So I think there must be a definite answer, not a range of answers.
So Sorry  for I   saw the wrong answer for the question
But yes the given answer = 20cm from the left lens then how's that coming?
hey after drawing ray diagrams and thinking I felt if the third lens was kept 20 cm to the left of left lens then object would be at optic centre ( an ideal situation I believe )
so there won't be any change in position of object or image. Still am I correct with the reason ?
Yes, placing the lens at that position does not change the position of the final image. However, you also need to explain why this increases the throughput of light, rather than having no effect on it.
sorry I don't know about throughput but I will try to read about that meanwhile if you come across the reason then please add the answer then.Regards

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