Mirror rotation refers to the act of physically turning a mirror around an axis. When a mirror rotates, the reflected light beam changes direction. Crucially, the angle of rotation of the reflected beam is twice the angle of rotation of the mirror itself. This is due to the law of reflection.
Explanation
Here's a breakdown:
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Normal: The normal is a line perpendicular to the surface of the mirror at the point where light strikes it.
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Angle of Incidence (i): The angle between the incident light ray and the normal.
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Angle of Reflection (r): The angle between the reflected light ray and the normal.
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Law of Reflection: The angle of incidence is equal to the angle of reflection (i = r).
When the mirror rotates, the normal also rotates by the same angle. Because the angle of incidence is measured relative to the normal, rotating the mirror changes the angle of incidence. The reflected ray then changes to maintain the equality of the angles of incidence and reflection with respect to the new normal.
How Mirror Rotation Affects Reflected Light
Let's say the mirror rotates by an angle θ.
- Normal Rotation: The normal rotates by the same angle, θ.
- Change in Incidence Angle: If the original angle of incidence was x, the new angle of incidence becomes x + θ.
- New Reflection Angle: According to the law of reflection, the new angle of reflection is also x + θ relative to the new normal.
- Total Beam Deflection: The difference between the new reflected ray's direction and the original reflected ray's direction is 2θ. This means the reflected beam rotates twice as much as the mirror itself.
Example
Imagine shining a laser beam onto a mirror. If you rotate the mirror by 5 degrees, the reflected laser beam will move by 10 degrees.
Applications
This principle of doubled angular deflection has various applications:
- Laser scanning: Rotating mirrors are used to sweep a laser beam across a surface.
- Optical instruments: They are employed in devices requiring precise beam steering.
- Scientific experiments: For manipulating light paths in research settings.
