Reflection and plane mirrors

Light rays and reflection

In geometric optics, light is modeled as rays. A ray is an idealized line showing the direction in which light energy travels. This model works well when the wavelength of light is much smaller than the objects and openings involved.

Reflection occurs when light reaches a surface and bounces back into the original medium. For a smooth surface, such as a mirror, reflection is organized and predictable. For a rough surface, reflection is diffuse: rays scatter in many directions.

The law of reflection

The law of reflection states that the angle of incidence equals the angle of reflection:

$heta_i= heta_r$

Both angles are measured relative to the normal, an imaginary line perpendicular to the surface at the point where the ray strikes.

The incident ray, reflected ray, and normal all lie in the same plane. This is why reflection problems can usually be drawn in two dimensions.

Specular and diffuse reflection

Specular reflection occurs from a smooth surface, where parallel incoming rays remain parallel after reflection. This produces clear images, as in a mirror.

Diffuse reflection occurs from rough surfaces. Each tiny part of the surface obeys the law of reflection, but because the local surface directions vary, reflected rays scatter in many directions. Diffuse reflection lets us see non-mirror objects from many viewing angles.

Plane mirror images

A plane mirror forms an image that appears behind the mirror. If an object is distance $d_o$ in front of the mirror, the image appears distance $d_i$ behind the mirror with

$d_i=-d_o$

The negative sign follows a common convention: virtual images are assigned negative image distance for mirrors.

The image is upright, the same size as the object, and laterally reversed. Lateral reversal means left and right appear switched relative to the object's own orientation, not that top and bottom are reversed.

Virtual images

A virtual image is formed when reflected or refracted rays appear to come from a point, but the rays do not actually pass through that point. The image in a plane mirror is virtual because light does not really come from behind the mirror.

Your eye traces reflected rays backward in straight lines and interprets them as coming from the virtual image location.

Ray diagrams

To draw a plane mirror ray diagram, choose a point on the object and draw at least two rays from it to the mirror. Reflect each ray using $heta_i= heta_r$. Extend the reflected rays backward behind the mirror. The extensions meet at the virtual image point.

Repeating this for enough object points gives the full image.

Reversibility of light paths

In geometric optics, light paths are reversible. If a ray can travel from point A to point B by reflection, it can travel from B to A along the same path in reverse. This principle helps explain image formation and optical alignment.

Reflection and Fermat's principle

The law of reflection can be derived from Fermat's principle, which states that light follows a path that makes travel time stationary. For reflection from a flat surface in a uniform medium, the shortest-time path has equal incidence and reflection angles.

This connects ray optics to a deeper variational principle.

The big idea

Reflection is governed by a simple geometric rule: angle in equals angle out, measured from the normal. Plane mirrors form upright virtual images located as far behind the mirror as the object is in front. Although reflection seems simple, it introduces key ideas used throughout optics: rays, normals, image formation, reversibility, and virtual images.