If you stand in front of the plane mirror at a distance of 1.3 m, what is the distance between your image and the mirror?

1. Break Down the Problem

To find the distance between a person's image and the mirror when standing at a distance of 1.3 meters, we need to consider how image formation works in a plane mirror. The image created by a plane mirror is located at the same distance behind the mirror as the object is in front of it.

2. Relevant Concepts

• Distance from the Object to the Mirror (d_object): The distance from you to the mirror is given as 1.3 m.
• Distance from the Mirror to the Image (d_image): In a plane mirror, the distance from the mirror to the image is equal to the distance from the object to the mirror.

Mathematically, the relationship can be expressed as: $d_{\text{image}} = d_{\text{object}} = 1.3 \, \text{m}$

3. Analysis and Detail

Since the distance to the mirror is 1.3 m, the distance from the image to the mirror is also 1.3 m. Thus, the total distance between you and your image is the sum of the distances from you to the mirror and from the mirror to your image.

4. Verify and Summarize

• The distance from you to the mirror: 1.3 m
• The distance from the mirror to your image: 1.3 m
• Therefore, the distance between you and your image is: $\text{Total Distance} = d_{\text{object}} + d_{\text{image}} = 1.3 \, \text{m} + 1.3 \, \text{m} = 2.6 \, \text{m}$

Final Answer

The distance between your image and the mirror is 1.3 m, but the total distance between you and your image is 2.6 m.