The minimum distance between an object and its real image formed by a convex lens is

Options

A. 1.5f
B. 2f
C. 2.5f
D. 4f

Answer

To find the minimum distance between an object and its real image formed by a convex lens, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Lens Formula**:
The lens formula for a convex lens is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
where \( f \) is the focal length of the lens, \( v \) is the image distance from the lens, and \( u \) is the object distance from the lens.

2. **Positioning the Object**:
To find the minimum distance between the object and its real image, we consider the case when the object is placed at the center of curvature (C) of the lens. The center of curvature is located at a distance of \( 2f \) from the lens.

3. **Finding the Image Position**:
When the object is at the center of curvature (C), the image is also formed at the center of curvature on the opposite side of the lens. Thus, the image distance \( v \) is also \( 2f \).

4. **Calculating the Distance**:
The distance between the object and the image can be calculated as:
\[ \text{Distance} = |u| + |v| = 2f + 2f = 4f \]

5. **Conclusion**:
Therefore, the minimum distance between the object and its real image formed by a convex lens is \( 4f \).

### Final Answer:
The minimum distance between an object and its real image formed by a convex lens is \( 4f \).

---