When a plane mirror at which a ray is incident is rotated through an angle \(\theta\), the reflected ray will be rotated through

When a plane mirror is rotated through an angle θ, the reflected ray will be rotated through an angle of 2θ. To understand why, imagine a ray of light hitting a plane mirror at an incident angle θ. The angle of incidence is the angle between the incident ray and the perpendicular to the mirror surface at the point of incidence. According to the law of reflection, the angle of reflection is equal to the angle of incidence, and the reflected ray makes the same angle with the perpendicular as the incident ray. Therefore, if we rotate the mirror through an angle θ, the perpendicular to the mirror at the point of incidence will also be rotated through an angle θ. This means that the angle of incidence will also change by θ. Now, since the angle of reflection is equal to the angle of incidence, the angle of reflection will also change by θ. Therefore, the angle between the incident ray and the reflected ray will change by 2θ (θ for the change in angle of incidence and θ for the change in angle of reflection). Hence, the reflected ray will be rotated through an angle of 2θ.