Attachment is given........ Show that the relative velocity of image in mirror 1 with respect to image in mirror 2 is 2vsin(beta)

To solve the problem of finding the relative velocity of the image in mirror 1 with respect to the image in mirror 2, we first need to understand the setup involving two mirrors and the concept of image formation. Let's break this down step by step.

Understanding the Setup

Imagine two mirrors positioned at an angle β to each other. When an object moves, it creates images in both mirrors. The images behave as if they are real objects, reflecting the motion of the actual object. The key here is to analyze how the images in each mirror relate to each other in terms of velocity.

Velocity of the Object

Let’s denote the velocity of the object as v. When the object moves, it creates images in both mirrors. The image in mirror 1 will have a velocity that is equal to the velocity of the object but in the opposite direction. Similarly, the image in mirror 2 will also reflect the object's motion.

Image Formation in Mirrors

• The image in mirror 1 (let's call it I1) is formed as if the object is located behind mirror 1.
• The image in mirror 2 (let's call it I2) is formed similarly, but behind mirror 2.

Calculating the Relative Velocity

To find the relative velocity of image I1 with respect to image I2, we need to consider their velocities. The velocity of I1 can be expressed as:

v = -v (since it moves in the opposite direction)