Draw a ray diagram to show the image formation by a combination of two thin convex lenses in contact. Obtain the expression for the power of this combination in terms of the focal lengths of the lenses.

In the above diagram, L1 and L2 are two convex lenses, O be the point object and I1 and I2 are the images obtained by the lens L1 and L2. Let P1 and P2 be the power of the lenses, and f1 and f2 be the focal lengths of the two lenses then,

1/f1 = 1/v1 - 1/u (1)

1/f2 = 1/v - 1/v1 (2)

By adding the equation (1) and (2)

1/v - 1/u = 1/f1 + 1/f2

So, We know that , P = 1/f

So P = 1/f1 + 1/f2

Then, P = P1 + P2.