Question

a converging and diverging lens of equal focal lengths are placed coaxially in contact find the focal length and power of the combination

Answer 1

sum of powers=1/f+1/(-f)
=0
focal length of combination=1/F=0
then
F=1/0=infinity

Answer 2

Power of the combination is zero.

Focal length of combination is infinity.

Explanation:

Given, we have a converging and a diverging lens of equal focal lengths placed coaxially in contact.

Focal length of diverging lens (concave) =  -f

Focal length of converging lens (convex) = f  

Power of the combination = Focal length of converging lens + Focal length of diverging lens = f - f = 0

Power of the combination is zero.

Focal length of combination = 1 / (Focal length of converging lens) + 1 / (Focal length of diverging lens)

1/F = 1 / f + 1/(-f) = 1/f - 1/f = 0

Hence F = 1/0 which is infinity.

Focal length of combination is infinity.