Assertion : Radius of curvature of a convex mirror is 20 cm. If a real object is placed at 10 cm from pole of the mirror, image is formed at infinity.
Reason : When object is placed at focus, its image is formed at infinity

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 solve the given problem, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that the radius of curvature of a convex mirror is 20 cm, and if a real object is placed at 10 cm from the pole of the mirror, the image is formed at infinity.

1. **Identify the parameters**:
- Radius of curvature (R) = 20 cm
- For a convex mirror, the focal length (F) is given by the formula:
\[ F = \frac{R}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm} \]
- The object distance (u) is -10 cm (the negative sign indicates that the object is in front of the mirror).

2. **Use the mirror formula**:
The mirror formula is given by:
\[ \frac{1}{F} = \frac{1}{u} + \frac{1}{v} \]
Substituting the known values:
\[ \frac{1}{10} = \frac{1}{-10} + \frac{1}{v} \]

3. **Rearranging the equation**:
\[ \frac{1}{v} = \frac{1}{10} + \frac{1}{10} = \frac{2}{10} = \frac{1}{5} \]
Thus,
\[ v = 5 \text{ cm} \]
Since v is positive, the image is formed on the same side as the object, which means the image is virtual and located 5 cm behind the mirror.

### Conclusion for Assertion
The assertion is **incorrect** because the image is not formed at infinity; it is formed at 5 cm behind the mirror.

### Step 2: Analyze the Reason
The reason states that when an object is placed at the focus, its image is formed at infinity.

1. **Understanding the condition**:
For a mirror, if the object is placed at the focus (F), the image is indeed formed at infinity. This is a general property of mirrors.

### Conclusion for Reason
The reason is **correct**.

### Final Conclusion
- Assertion (A) is false.
- Reason (R) is true.

Thus, the correct answer is option 4: A is false and R is true.

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