A concave lens is placed in contact with a convex lens of focal length `25 cm`. The combination produces a real image at a distance of `80 cm`, when an object is at a distance of `40 cm`. What is the focal length of concave lens ?

Explanation

To find the focal length of the concave lens in the given problem, we can follow these steps:

### Step 1: Understand the given information
We have a convex lens with a focal length \( f_1 = +25 \, \text{cm} \) and a concave lens with an unknown focal length \( f_2 \). The object distance \( u = -40 \, \text{cm} \) (negative as per the sign convention) and the image distance \( v = +80 \, \text{cm} \) (positive because it is a real image).

### Step 2: Use the lens formula for the combination
The lens formula for a lens is given by:
\[
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