Assertion : Focal length of a convex mirror is 20 cm. If a real object is placed at distance 20 cm from the mirror, its virtual erect and diminished image will be formed.
Reason : If a virtual object is placed at 20 cm distance, its image is formed at infintiy.

Options

A. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason given in the problem statement regarding the convex mirror.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the focal length of a convex mirror is 20 cm and that if a real object is placed at a distance of 20 cm from the mirror, a virtual, erect, and diminished image will be formed.

2. **Identify the Sign Convention**:
- For mirrors, the focal length (f) of a convex mirror is positive. Therefore, \( f = +20 \, \text{cm} \).
- The object distance (u) for a real object placed in front of the mirror is negative, so \( u = -20 \, \text{cm} \).

3. **Using the Mirror Formula**:
- The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
- Substituting the known values:
\[ \frac{1}{20} = \frac{1}{v} + \frac{1}{-20} \]
- Rearranging gives:
\[ \frac{1}{v} = \frac{1}{20} + \frac{1}{20} = \frac{2}{20} = \frac{1}{10} \]
- Therefore, \( v = 10 \, \text{cm} \).

4. **Analyzing the Image Characteristics**:
- Since \( v \) is positive, the image is virtual.
- The image is also erect and diminished because the magnification \( m \) can be calculated as:
\[ m = -\frac{v}{u} = -\frac{10}{-20} = \frac{1}{2} \]
- Since \( m \) is positive, the image is erect, and since \( |m| < 1 \), the image is diminished.

5. **Conclusion for the Assertion**:
- The assertion is true: A virtual, erect, and diminished image is formed when a real object is placed at 20 cm from the convex mirror.

6. **Understanding the Reason**:
- The reason states that if a virtual object is placed at 20 cm distance, its image is formed at infinity.
- In the context of mirrors, if we consider a virtual object, we can set \( u = +20 \, \text{cm} \) (since the virtual object is behind the mirror).
- Using the mirror formula again:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
- Substituting \( f = +20 \, \text{cm} \) and \( u = +20 \, \text{cm} \):
\[ \frac{1}{20} = \frac{1}{v} + \frac{1}{20} \]
- Rearranging gives:
\[ \frac{1}{v} = \frac{1}{20} - \frac{1}{20} = 0 \]
- This implies \( v \) approaches infinity, confirming that the image is formed at infinity.

7. **Conclusion for the Reason**:
- The reason is also true: A virtual object placed at 20 cm results in an image formed at infinity.

8. **Final Conclusion**:
- Both the assertion and reason are true, but the reason does not correctly explain the assertion.

### Final Answer:
- Both the assertion and reason are true, but the reason is not a correct explanation for the assertion.