Write the law of reflection of a light beam from a mirror in vector form, using the directing unit vectors e and e' of the incident and reflected beams and the unit vector n of the outside normal to the mirror surface.

The law of reflection describes how a light beam behaves when it strikes a mirror. In vector form, this law can be expressed using the unit vectors for the incident beam, reflected beam, and the normal to the mirror surface.

Vector Representation

Let:

• e = unit vector of the incident beam
• e' = unit vector of the reflected beam
• n = unit vector of the normal to the mirror surface

Law of Reflection

The law of reflection states that the angle of incidence is equal to the angle of reflection. In vector form, this can be mathematically represented as:

e' = e - 2(e · n)n

Explanation of the Formula

In this equation:

• e · n calculates the dot product of the incident vector and the normal vector, giving the component of the incident vector along the normal.
• 2(e · n)n represents twice this component, which is subtracted from the incident vector to find the reflected vector.

This formula effectively captures the essence of how light reflects off a surface, adhering to the principle that the angles are equal relative to the normal. Understanding this relationship is crucial in fields like optics and physics.