Angular Velocity of the Reflected Beam in a Rotating Plane Mirror

When a light beam strikes a plane mirror, it follows the laws of reflection, which state that the incident angle is equal to the reflected angle. However, when the plane mirror is rotating, the angle of incidence and the angle of reflection will change due to the rotation. Consequently, the angular velocity of the reflected beam will also be affected.

Angular Velocity and Rotation
Angular velocity measures the rate at which an object rotates around a fixed axis. It is defined as the change in angular displacement per unit time. In this case, the plane mirror is rotating at an angular velocity of 2 rad/s.

The Law of Reflection
The law of reflection states that the angle of incidence is equal to the angle of reflection. When a light beam strikes the plane mirror, it forms an incident angle with the mirror's surface. This incident angle determines the direction of the reflected beam.

Effect of Rotation on the Incident Angle
Due to the rotation of the plane mirror, the angle of incidence will continuously change. As the mirror rotates, the reflected beam will be displaced, resulting in a different incident angle. Therefore, the angular velocity of the reflected beam will be affected by the rotation of the mirror.

Determining the Angular Velocity of the Reflected Beam
To determine the angular velocity of the reflected beam, we need to consider the relationship between the angular velocity of the mirror and the angular velocity of the reflected beam. The angular velocity of the reflected beam can be calculated using the formula:

Angular velocity of the reflected beam = Angular velocity of the mirror + Angular velocity due to displacement

The angular velocity due to displacement is caused by the change in position of the reflected beam as the mirror rotates. This angular velocity can be determined by considering the linear velocity of the mirror's surface and the distance between the incident and reflected beams.

Conclusion
In conclusion, the angular velocity of the reflected beam in a rotating plane mirror is determined by the angular velocity of the mirror and the angular velocity due to displacement caused by the rotation. By considering the laws of reflection and the effects of rotation, we can calculate the angular velocity of the reflected beam.

I think angular velocity of reflected beam will be 4 red/s becz when mirror is rotated by x degree by keeping incident ray fixed, then reflected ray rotated by 2x degree