To solve the problem, we need to understand how images are formed in a plane mirror and how the distance between the object (the man) and the image changes when the mirror is moved. ### Step-by-Step Explanation 1. **Initial Setup**: - The man is standing 4 meters in front of a plane mirror. - In a plane mirror, the image formed is at the same distance behind the mirror as the object is in front of it. Therefore, the initial distance from the man to his image is: \[ \text{Distance to image} = \text{Distance to mirror} + \text{Distance behind mirror} = 4m + 4m = 8m \] 2. **Moving the Mirror**: - The mirror is then moved 1 meter towards the man. This means the new distance from the man to the mirror is: \[ \text{New distance to mirror} = 4m - 1m = 3m \] - The image will still be formed at the same distance behind the new position of the mirror. Therefore, the new distance from the man to his image is: \[ \text{New distance to image} = \text{New distance to mirror} + \text{Distance behind new mirror} = 3m + 3m = 6m \] 3. **Final Calculation**: - Thus, the distance between the man and his new image after the mirror has been moved is 6 meters. ### Conclusion The correct answer is **C. 6m**. ### Explanation of Other Options - **A. 3m**: This option is incorrect because it does not account for the distance of the image behind the mirror. The distance to the image must always be equal to the distance from the object to the mirror. - **B. 5m**: This option is also incorrect. It seems to suggest a misunderstanding of how the distances are calculated. The distance to the image is not simply the distance to the mirror minus some value; it must consider the image's position behind the mirror as well. - **D. 10m**: This option is incorrect as it assumes that the distance to the image would double the distance to the mirror after it has been moved, which is not the case. The image distance is always equal to the object distance from the mirror. ### Common Pitfalls - **Misunderstanding Image Formation**: Students often forget that the image distance is equal to the object distance from the mirror. This can lead to incorrect calculations. - **Not Adjusting for Mirror Movement**: When the mirror is moved, it’s crucial to recalculate the distance from the man to the new position of the mirror before determining the new image distance. ### Revision Summary - The distance to the image in a plane mirror is equal to the distance from the object to the mirror. - When the mirror is moved, recalculate the distance from the object to the new mirror position. - The total distance between the object and the image is the sum of the distances to the mirror and behind the mirror. - Always double-check calculations to avoid common mistakes related to image formation in mirrors.