When two or more lenses are used in an optical system, the formula used to calculate the magnification of the final image produced by the system is:

M_system = (M_{lens #1})(M_{lens #2})(M_{lens #3}) ....

 

When an optical system uses two lens, work each lens separately. Remember that the image of lens #1 will serve as the object for lens #2. If the image of lens #1 falls "in front of" lens #2, you can calculate the object distance for lens #2 by subtracting the value of d_i for lens #1 from the total distance separating the two lenses.

 

In this example, two converging lens produce a final image which is real and upright. A scaled diagram would be necessary to determine how the height of the final image, I₂, compares to the height of the original object, O.

 

A similar process will produce the image for a double lens system involving a converging and a diverging lens.

 

 

In this second example, a converging lens followed by a diverging lens produce a final image which is virtual and inverted. A scaled diagram would be necessary to determine how the height of the final image, I₂, compares to the height of the original object, O.