Effective Focal Length of Two Thin Lenses

[Chadlee88]

Question: Two thin lenses with focal lengths of 16cm and 18cm respectively are placed 12cm apart. what is the effective focal length of this combination of lenses?

I used the formula:

1/f1+ 1/f2 = 1/f effective

My solution:

1/16 + 1/18 = 1/f effective

which gave me an effective focal length of 8.47cm.

Is this right or does the fact that they are put 12cm apart affect the effective focal length?

 

[Hootenanny]

Your solution assumes that the two lenses are in contact with each other, i.e. there is no distance between the two lenses. What you need is the back focal length, which is the distance from the second lens to the combined focal length of the two lenses.

 

[lpfr]

Hootenanny is right.
Draw a diagram. Apply twice the formula 1/f=1/a+1/b. The first time, to find were the first lens forms the image. Draw this position in the diagram. The second time, to find were the second lens forms the image of the {image formed by the first lens}.
Beware of signs!