Calculate the position that a lens should be placed in order to achieve the maxi

Question

Calculate the position that a lens should be placed in order to achieve
the maximum magnification. The length between the object plane and the image plane
is 40cm and are fixed. Only the lens can be moved. The focal length of the lens is 10cm

1) What is S and S'
2) What is the position of the lens
3) what is the maximal magnification possible?
4) what is the smallest magnification under same conditions?
5) Give a real life example where this problem could be encountered

please show all work to receive 5 stars, thanks!!!

Explanation / Answer

Light rays obey the Law of Reflection when they encounter plane mirrors. The path of the ray is sketched below. Using geometry a + ß + ? = p (1) ? + ß = ½p (2) ? + f = ½p (3) ? = p - 2? - 2f (4) Using the first three equations to eliminate ? and f from equation (4), we find ? = p - 2a

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