If the image formed by a lens is always virtual, erect and smaller than the object, what is the nature of the lens ?

Answer

To determine the nature of the lens that forms a virtual, erect, and smaller image than the object, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Image Characteristics**:
- The problem states that the image is virtual, erect, and smaller than the object.
- Virtual images are formed when the light rays do not actually converge but appear to diverge from a point.

2. **Identifying Lens Types**:
- There are two main types of lenses:
- **Convex Lens**: Can form real or virtual images depending on the position of the object.
- **Concave Lens**: Always forms virtual images that are erect and smaller than the object.

3. **Analyzing the Concave Lens**:
- When an object is placed in front of a concave lens, the rays of light diverge after passing through the lens.
- The image formed by a concave lens is always virtual, meaning it cannot be projected on a screen.
- The image is also erect (upright) and smaller than the object, which matches the conditions given in the question.

4. **Conclusion**:
- Since the characteristics of the image (virtual, erect, and smaller) align perfectly with the behavior of a concave lens, we conclude that the nature of the lens in question is a **concave lens**.

### Final Answer:
The nature of the lens is **concave**.

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