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I am given a small piece of lens which is tightly sealed and there are two lenses at the end and I do not know what is in between.

My question is as follow. If I design a small apparatus of object and get the image then will I be able to design a similar system that gives me the same magnification?

I measured the object and its image with simple ruler and light source and get the magnification by dividing the image length by the size of the object. Based on my poor memory in optics I was expecting to get the same ratio by dividing the distance of the object and the image but these two numbers are not equal.

Do I have to consider more advanced relations and matrix computation perhaps due to the existence of thick lenses?

Again I am not allowed to break the device and I am not sure about the nature and dimension of lenses and the number of lenses inside.

Any help and advice is greatly appreciated.