Assertion : The minimum distance between an object and its real image formed by a convex lens is 2f.
Reason : The distance between an object and its real image is minimum when its magnification is - 1.

Options

A. If both assertion and reason are true and\ reason is a correct explanation of the assertion
B. If both assertion and reason are true but the reason is not a correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true

Answer

To analyze the assertion and reason provided in the question, we will break down the steps systematically.

### Step-by-Step Solution

1. **Understanding the Assertion**: The assertion states that the minimum distance between an object and its real image formed by a convex lens is 2f. We need to verify if this is true.

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

3. **Setting Up the Distances**: Let the object distance be \( u = -x \) (negative as per sign convention) and the image distance be \( v \). The distance \( D \) between the object and the image can be expressed as:
\[ D = v - (-x) = v + x \]

4. **Rearranging the Lens Formula**: Substituting \( u \) into the lens formula, we get:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{x} \]
Rearranging gives:
\[ \frac{1}{v} = \frac{1}{f} - \frac{1}{x} \]

5. **Finding the Relationship Between Distances**: Cross-multiplying gives:
\[ \frac{vx}{f} = v - x \]
Rearranging leads to:
\[ vx - fx = fv \]
or:
\[ x(v - f) = fv \]

6. **Finding Minimum Distance**: To find the minimum distance \( D \), we need to consider the condition when the magnification \( m = -1 \). The magnification for a lens is given by:
\[ m = -\frac{v}{u} \]
Setting \( m = -1 \) implies \( v = -u \). Thus, \( v = x \).

7. **Substituting Back**: Substituting \( v = x \) back into the equation gives:
\[ D = v + x = x + x = 2x \]
Since \( x \) corresponds to the object distance when the magnification is -1, we need to find the relationship between \( x \) and \( f \).

8. **Finding the Minimum Value**: The minimum distance occurs when the object is at the center of curvature (2f), leading to:
\[ D = 2f \]
But this is not the correct interpretation for the minimum distance between the object and its real image.

9. **Conclusion on Assertion**: The correct minimum distance between the object and its real image formed by a convex lens is actually 4f, not 2f. Therefore, the assertion is **false**.

10. **Analyzing the Reason**: The reason states that the distance between an object and its real image is minimum when its magnification is -1. This is true because when the magnification is -1, the image size equals the object size, and this occurs when the object is at the center of curvature.

### Final Conclusion
- **Assertion**: False
- **Reason**: True