Introduction:
When a bird is flying with a velocity v between two long vertical plane mirrors, it creates multiple images due to multiple reflections. In this scenario, we need to find the relative velocity of approach between the images due to the first reflection in each mirror.

Explanation:
To calculate the relative velocity of approach between the images, we need to consider the angles of incidence and reflection, and apply the laws of reflection.

1. Angle of Incidence:
The angle of incidence is the angle between the incident ray and the normal to the mirror at the point of incidence. In this case, the angle of incidence for the first mirror (m1) is T-Ta, where T is the angle of approach of the bird and Ta is the angle between the incident ray and the normal to mirror m1.

2. Angle of Reflection:
The angle of reflection is the angle between the reflected ray and the normal to the mirror at the point of incidence. According to the laws of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection for the first mirror (m1) is also T-Ta.

3. First Reflection:
When the incident ray from the bird strikes the first mirror (m1), it reflects back at an angle equal to the angle of incidence (T-Ta). This reflected ray creates an image of the bird in mirror m1.

4. Image Formation:
The image formed in mirror m1 due to the first reflection will be at the same distance behind the mirror as the bird is in front of the mirror. The image will also be at the same height as the bird.

5. Relative Velocity of Approach:
To calculate the relative velocity of approach between the images, we need to consider the distance between the bird and the image formed in mirror m1. This distance is equal to twice the distance between the bird and mirror m1.

The relative velocity of approach between the images due to the first reflection in each mirror can be calculated using the formula:
Relative Velocity of Approach = (Velocity of the Bird - Velocity of the Image) / Distance between the Bird and the Image

Conclusion:
By considering the laws of reflection and the concept of image formation in mirrors, we can calculate the relative velocity of approach between the images due to the first reflection in each mirror. This relative velocity depends on the velocity of the bird, the angles of approach and reflection, and the distance between the bird and the image formed in mirror m1.