Assertion : When object moves in a direction perpendicular to a fixed plane mirror then velocity of image with respect object is double in magnitude to the magnitude of velocity of object.
Reason : Distance of image from the plane mirror is always same as distance of object from the plane mirror.

Options

A. If both assertion and reason are correct and rason is a correct explanation of the assertion.
B. If both assertion and reason are correct but reason is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect.
D. If assertion is incorrect but reason is correct.

Answer

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

### Step 1: Understanding the Assertion
The assertion states that when an object moves in a direction perpendicular to a fixed plane mirror, the velocity of the image with respect to the object is double the magnitude of the velocity of the object.

1. **Setup the scenario**:
- Consider a plane mirror and an object moving perpendicular to it.
- Let the object move with a velocity \( v \) in the direction perpendicular to the mirror.

### Step 2: Analyzing the Image Movement
2. **Image formation**:
- The image formed by a plane mirror is located at the same distance behind the mirror as the object is in front of it.
- If the object moves a distance \( d \) in time \( t \), the image also moves the same distance \( d \) in the opposite direction.

### Step 3: Relative Velocity Calculation
3. **Calculate relative velocity**:
- If the object moves a distance \( d \) in time \( t \), then its velocity \( v = \frac{d}{t} \).
- The image also moves the same distance \( d \) in the same time \( t \), thus the image's velocity is also \( v \) but in the opposite direction.
- Therefore, the relative velocity \( v_{relative} \) between the object and the image is:
\[ v_{relative} = v + v = 2v \]
- This shows that the velocity of the image with respect to the object is indeed double the magnitude of the velocity of the object.

### Step 4: Understanding the Reason
4. **Analyzing the Reason**:
- The reason states that the distance of the image from the plane mirror is always the same as the distance of the object from the plane mirror.
- This is true because the image distance \( d_i \) is equal to the object distance \( d_o \) from the mirror.

### Step 5: Conclusion
5. **Final Conclusion**:
- Both the assertion and the reason are correct.
- The reason correctly explains the assertion because the equality of distances leads to the doubling of the relative velocity.

### Final Answer:
- **Assertion**: True
- **Reason**: True
- **Explanation**: The reason is the correct explanation of the assertion.

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