Two convex lenses of focal length f1 and f2 are in contact with each other. Find their equivalent focal length.
consider two convex lenses in contact such that their separation is very small as compared to their focal length.
Let a point object "O" is placed at a distance "p1" from the lenses L1 whose real image I1 is formed at a distance q1.
Using thin lens formula
Image servers as a virtual object for the second lens. If we neglect small distance between the lenses ,the distance of this virtual object from lens L2 will be the same as its distance from L1. If L2 forms an image I2 of this virtual object
at a distance q2 then p2.
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Adding equation (1) and equation (2)

now if we replace the two lenses of focal lengths"f1" and "f2" by a single lens of focal length "f" such that it forms an image at a distance q2 of an object placed at a distance p1 from it as shown such lens is called equivalent lens and
Its focal length is known as equivalent focal length. For the above lens
comparing equation (3) and equation (4) , we get
If f1>f2 the combined lens behaves as a concave lens.
If f2> f1 the combined lens behaved as a convex lens.
Note : above two conditions are valid if one lens is convex and the other is concave lens . If both lenses are convex then the combined lens will behave like a convex lens.
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