If the distance between the images formed on the plane mirror of the object A1 and A2 correspondingly is 10 cm what distance between the object A1 and A2?

1. Break Down the Problem

To find the distance between objects A1 and A2 based on the distance between their images formed by a plane mirror, we first need to understand the relationship between the object distances and image distances in the context of plane mirrors.

2. Relevant Concepts

• In a plane mirror, the image formed of an object is located at the same distance behind the mirror as the object is in front of it.
• Thus, if an object is at a distance $d$ from the mirror, the image is also at a distance $d$ behind the mirror.
• Therefore, if we have two objects A1 and A2 in front of the mirror, and their images are formed such that the distance between these images is known, we can apply the relationship: $\text{Distance between images} = (\text{Distance of A1 from mirror}) + (\text{Distance of A2 from mirror})$

3. Analysis and Detail

Given that the distance between the images of the objects A1 and A2 is 10 cm, let:

• $d_1$ be the distance of object A1 from the mirror.
• $d_2$ be the distance of object A2 from the mirror.

The distance between the images $I_1$ and $I_2$ can be expressed as: $I_1 I_2 = d_1 + d_2$ Since we know $I_1 I_2 = 10$ cm, we can use this to express the sum of the distances from the mirror.

To find the distance $D$ between the objects A1 and A2, we have: $D = |d_1 - d_2|$

4. Verify and Summarize

Assuming that either $d_1$ or $d_2$ could be derived from $d_1 + d_2 = 10$ cm, the exact values of $d_1$ and $d_2$ are not specified, making it impossible to calculate $D$ explicitly without additional information. However, the maximum distance between A1 and A2 occurs when one object is at 0 cm and the other is at 10 cm: $D = |0 - 10| = 10 \text{ cm}$ Conversely, if both are equidistant from the mirror at 5 cm each, $D = 0$ cm. Hence, the distance could range from 0 to 10 cm.

Final Answer

The possible distance between the objects A1 and A2 is between 0 cm and 10 cm, depending on their individual distances from the mirror.