Suppose there are two lenses touching each other as shown in the diagram below. the focal length of the lenses are $f_1$ and $f_2$ respectively. Now by using the formula for lens combination I obtained the final focal length as $$\frac{f_1f_2}{f_1+f_2}$$.
Now suppose I assume there is a very small distance between them say d,where $d\ll R$, and I calculate the focal length of the system I still obtain the same result. Now my question is whether I can conclude from this that when ever two optical devices(lens,prism,etc) are touching each other. Can I do the calculation by assuming there is a small distance between them?