Question

If two lenses are joined then focal length ??

Answer 1

it depends particularly on the lenses which type lens they r

Answer 2

f you have two thin lenses “in contact”, you actually have two thin lenses on the same place. Of course then their strengths (focal powers = inverse of focal length) just add.

If you have real lenses, this can vary a bit more. Here an example:

As you can see, the addition of a lens of power +10D and one of -5D doesn’t yield +5D as it “should”, but actually more, about 6.3D in this case. This is the case because with real lenses, you have to look not whether their sides are in contact, but whether their principal planes are in contact. The right principal plane of the left lens (blue) would need to be in contact with the left principal plane of the right lens. Alas, they are not, thus you get a different power through application of the formula

p1234=p12+p34−p12p34(PL34−PR12)

You can also get the exact opposite behaviour and get a smaller value than expected, here 3.86D: