A 50 cm tall object is at a very large distance from a diverging lens. A virtual, erect and diminished image of the object is formed at a distance of 20 cm in front of the lens. How much is the focal length of the lens?

Explanation

To find the focal length of the diverging lens given the object height, image distance, and the nature of the image formed, we can use the lens formula and magnification formula.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Height of the object (h_o) = 50 cm
- Distance of the image from the lens (v) = -20 cm (negative because it’s a virtual image formed on the same side as the object)
- The object is at a very large distance, which means we can consider the object distance (u) to be approximately -∞.
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