Reflection (Geometrical Optics)

Laws of light reflection on flat and curved surfaces, angles of incidence and reflection.

Conceptual context

Reflection of light is the phenomenon by which a luminous ray changes direction upon encountering a surface without passing through it. It underpins all mirror optics and numerous everyday devices, from rear-view mirrors to reflecting telescopes. Understanding reflection allows one to predict exactly where light travels after striking a surface and explains phenomena as diverse as image formation in a mirror or signal transmission in optical fiber.

Within geometrical optics, reflection is treated as an instantaneous change in the ray's direction at the contact point with the surface, without considering wave effects. This idealization holds whenever the surface is smooth at the scale of the wavelength.

🟢 Essential level

When a ray of light reaches a polished surface, it bounces. The direction of the bounce is not arbitrary: the reflected ray leaves at the same angle to the perpendicular of the surface as the angle at which it arrived. That perpendicular is called the normal, and angles are always measured from it, not from the surface itself.

This rule is universal: it works equally for a bathroom mirror, the surface of a calm lake or a metallic sheet. The incident ray, the normal and the reflected ray share the same plane, and the angles $\theta_i$ and $\theta_r$ are identical. If light arrives perpendicularly, it returns along the same path; if it arrives at an angle, it reflects with the same inclination on the other side of the normal.

An everyday example makes this clear: pointing a flashlight at a wall mirror moves the spot of light on the floor as the flashlight tilts, but always in a predictable way, because the outgoing angle exactly copies the incoming one. That is why a simple hand mirror can direct a beam of sunlight onto a chosen spot just by controlling its tilt, with no calculation needed beyond that equality of angles.

🔵 Formal level

Basic formulas

The law of reflection is stated as an exact equality between angles:

Law of reflection

This relationship establishes that $\theta_r$ always replicates $\theta_i$, regardless of the nature of the reflecting material or the wavelength of the light. The angles are measured in the plane of incidence, defined by the incoming ray and the surface normal at the contact point. The law is complemented by the coplanarity condition: incident ray, normal and reflected ray belong to the same plane.

Real student questions

Why is the angle measured from the normal and not from the surface? Because the normal is unique and perpendicular to the surface at each point, defining an angle without ambiguity. On curved surfaces, the tangent changes continuously but the local normal is always well defined.

Does the law of reflection work with any type of light? Yes. The law is independent of wavelength, intensity or polarization. These factors affect how much light is reflected (Fresnel coefficients), but not the direction of the reflected ray.

What happens if the surface is not perfectly smooth? Each point on the surface reflects according to its local normal. If the normals are disordered (rough surface), the reflected rays emerge in many directions: this is diffuse reflection. The law still holds locally, but the macroscopic effect is scattering.

Is total internal reflection truly total? In classical geometrical optics, yes. In wave optics, an evanescent wave penetrates a distance of the order of the wavelength into the second medium, but it carries no net energy if the second medium is infinite.

Final synthesis

Reflection is the most elementary and most exact optical phenomenon: a single symmetry principle (equality of angles with respect to the normal) governs the behavior of light bouncing off any specular surface. The critical angle extends this principle to the regime of total confinement, connecting geometrical optics with waveguide technology and optical communications.