A man stands 4m in front of a plane mirror. If the mirror is moved 1m towards the man, the distance between him and his new image is?

Analyze the question: A man stands 4 m from a plane mirror. The mirror is moved 1 m towards him. We need the distance between the man and his new image.

Concept: A plane mirror forms a virtual image as far behind the mirror as the object is in front of it. So the distance between the object and its image is twice the object's distance from the mirror.

Solution:

1. Initial distance from man to mirror = 4 m.
2. The mirror moves 1 m towards the man, so the new distance = 4 − 1 = 3 m.
3. The image is 3 m behind the mirror.
4. Distance between man and image = 3 + 3 = 6 m.

Common mistakes:

• Choosing 3 m, which is only the man-to-mirror distance and forgets to add the image distance.
• Choosing 5 m or 10 m by adding the 1 m movement instead of subtracting it, or by using the original 4 m (4 + 4 = 8 m) incorrectly.

Exam tip: For plane mirror questions, always do two steps: find the new object-to-mirror distance, then double it. If the mirror moves by x towards the object, the object-to-image distance decreases by 2x. Here it changes from 8 m to 6 m.