Show with a simple diagram that when a mirror with a fixed...

Show with a simple diagram that when a mirror with a
fixed beam incident upon it is rotated through a certain
angle, the reflected beam is rotated through an angle
twice as large. (This doubling of displacement makes
irregularities in ordinary window glass more evident.)

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Key Concepts

Law of Reflection

This principle states that the angle of incidence is equal to the angle of reflection when a light ray strikes a surface. It is fundamental in predicting the path of a light beam when it interacts with a mirror and forms the basis for understanding how the direction of the reflected beam changes upon rotation of the mirror.

Normal Line

The normal line is an imaginary line perpendicular to the surface at the point of incidence. The law of reflection uses the normal to measure the angle of incidence and reflection, and any rotation of the mirror directly affects the orientation of the normal, thereby influencing the path of the reflected beam.

Angular Doubling Effect

When the mirror is rotated by a certain angle, the normal rotates by the same angle. Since the angle of reflection relative to the normal must remain equal to the angle of incidence, the overall effect is that the reflected beam rotates by twice the angle of rotation of the mirror. This doubling effect makes small changes in the mirror's orientation, such as those due to imperfections in ordinary window glass, more evident.

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