Choose the correct option(s). Assume all lenses in air.

Options

A. a.if a lens always forms real image for a virtual object, it is concave.
B. b.if a lens forms magnified image for a virtual object the lens is concave
C. c.if a lens forms magnified image for a virtual object, the lens is convex.
D. d.if a lens always forms real image for a virtual object it is convex.

Explanation

To solve the question, we need to analyze the behavior of convex and concave lenses when dealing with virtual objects and determine which options are correct based on the properties of these lenses.

### Step-by-Step Solution:

1. **Understanding Lenses**:
- A **convex lens** converges light rays that are incident on it, and it can form both real and virtual images depending on the position of the object.
- A **concave lens** diverges light rays, and it typically forms virtual images for real objects.

2. **Real and Virtual Objects**:
- A **real object** is an object from which light rays actually diverge.
- A **virtual object** is an object from which light rays appear to diverge, but they do not actually come from that point.

3. **Convex Lens Behavior with Virtual Objects**:
- When a convex lens has a virtual object (i.e., the object is located between the focal point and the lens), it can produce a real image on the opposite side of the lens. This image is typically diminished.

4. **Concave Lens Behavior with Virtual Objects**:
- A concave lens, when presented with a virtual object, can produce a virtual image that is magnified. However, it cannot produce a real image from a virtual object.

5. **Evaluating the Options**:
- **Option A**: "Concave lens always forms real images for virtual objects." - This is incorrect. Concave lenses do not form real images from virtual objects.
- **Option B**: "Concave lens can magnify images for virtual objects." - This is correct. Concave lenses can produce magnified virtual images.
- **Option C**: "Convex lens magnifies images for virtual objects." - This is incorrect. While convex lenses can produce images from virtual objects, they typically do not magnify them.
- **Option D**: "Convex lens always forms real images for virtual objects." - This is correct. A convex lens can form real images from virtual objects.

6. **Conclusion**:
- The correct options are **B** and **D**.