A convex lens of focal length 25 m is placed coaxially in contact with a concave lens of focal length 20 cm. Determine the power of the combination. Will the system be converging or diverging in nature?

The net focal length of the combination is
1/f = 1/f1 + 1/f2 = 1/2500 + 1/-20 = 1/2500 - 1/20
To solve this, we need to find a common denominator:
1/f = (20 - 2500) / (2500 * 20) = -2480 / 50000 = -248/5000 = -62/1250 cm
f = -1250/62 cm ≈ -20.16 cm
Power of combination = P = P1 + P2 = 1/f1 + 1/f2
P = 1/25 + 1/-0.20 = 1/2.5 + 1/-0.20 = 0.4 - 5 = -4.6 D
Alternatively, using the calculated focal length:
P = 1/f = 1/(-1250/62) = 62/-1250 = -0.0496 D ≈ -4.96D
Since power is negative, the combination is diverging.