A converging lens of focal length `50 cm` is placed co-axially in contact with another lens of unknown focal length. If the combination behaves like a diverging lens of focal length `50 cm`, find the power and nature of second lens.

Explanation

To solve the problem step by step, we will follow the principles of lens optics.

### Step 1: Understand the Given Information
We have a converging lens with a focal length \( f_1 = 50 \, \text{cm} \) and another lens with an unknown focal length \( f_2 \). The combination of these two lenses behaves like a diverging lens with a focal length of \( f = -50 \, \text{cm} \).

### Step 2: Convert Focal Lengths to Power
The power \( P \) of a lens is given by the formula:
\[
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