Two convex lenses A and B of focal lengths 20 cm and 10 cm are placed coaxially 10 cm apart. An object is placed on the common axis at a distance of 10 cm from lens A. Find the position and magnification of the final image.

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From figure below, we have, for lens A
f₁ = + 20 cm and u₁ = –10 cm
The image distance v₁ is given by
which gives                      
                                            
Thus, a virtual image is formed at I₁ at a distance of 20 cm from lens A, if the lens B were absent. This image acts as a virtual object for lens B which forms the final image at I₂ at a distance v₂ from lens B.
For lens B we have,
x = 10 cm, u₂ = – (20 + 10) = –30 cm f₂ = + 10 cm.


The image distance v₂ is given by
                               
which gives                 
Thus, a real image I₂ is formed at a distance of 15 cm from lens B.
Magnification due to 
Magnification due to 
Magnification of the final image is
                                  
This shows that the final image is inverted and is of the same size as the object.