A converging and a diverging lens of equal focal lengths . . . .

Question : A converging and a diverging lens of equal focal lengths are placed coaxially in contact. Find the power and focal length of the combination.

Doubt by Angad

Solution : 

Let the focal length of converging and diverging lens be f1 and f2 and the equivalent length of the combination would be F.

f₁ = +f

f₂ = -f

We know

1/F = 1/f₁+1/f₂

1/F = 1/f + 1/(-f)
1/F = 0
F = ∞

Equivalent Power 
P = 1/F
P = 1/∞
P = 0