A ray of light impinges on a mirror as shown in Figure P 18.11 . A second mirror is fastened at

step 1 In this question, we have two mirrors. There are 90 degrees to each other. And then a light ray

A ray of light impinges on a mirror as shown in Figure P...

A ray of light impinges on a mirror as shown in Figure $\mathrm{P} 18.11 .$ A second mirror is fastened at $90^{\circ}$ to
the first. After striking both mirrors, at what angle relative to the incoming ray does the outgoing ray emerge?

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Key Concepts

Geometric Transformation by Reflections

Reflecting an object or ray across a line is a type of geometric transformation. When two such reflections are applied in sequence, they result in a rotation, rather than a simple reflection. This concept allows complex reflection systems to be simplified into equivalent rotational effects, making it easier to determine the overall change in the ray’s direction after multiple reflections.

Law of Reflection

The law of reflection states that when a light ray strikes a reflective surface, the angle at which it hits the surface (the angle of incidence) is equal to the angle at which it reflects away (the angle of reflection). This fundamental rule is used to analyze and predict the paths of rays in various optical setups, including multiple mirror systems.

Successive Reflections and Rotation Effect

When light reflects off two mirrors in succession, the combined effect can be interpreted as a single rotation of the ray’s direction. Specifically, reflecting off two mirrors whose surfaces are at an angle relative to each other results in an effective rotation of the ray’s path by twice the angle between the mirrors. In the case of perpendicular mirrors, this means the outgoing ray’s direction is rotated by 180 degrees relative to the incident ray, so it emerges in the opposite direction.

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