25.2 The Law of Reflection

The Law of Reflection

Light reflection describes how light bounces off surfaces. It's the reason you can see yourself in a mirror, spot a glare off a window, or watch a sunset reflected on a lake. The law of reflection gives you a simple, precise rule for predicting the direction light travels after hitting a surface.

Reflection from Surface Types

Not all surfaces reflect light the same way. The difference comes down to how smooth or rough the surface is at a microscopic level.

Specular reflection happens on smooth surfaces. All incoming rays hitting at the same angle reflect at the same angle, producing a clear, mirror-like reflection. Think of a plane mirror, polished metal, or the surface of still water.

Diffuse reflection happens on rough surfaces. Even though each individual ray still obeys the law of reflection, the surface has tiny irregularities pointing in different directions. This scatters the reflected light, so you don't see a sharp image. Paper, matte paint, and unpolished wood all produce diffuse reflection.

The Law of Reflection and the Normal

The normal is an imaginary line drawn perpendicular to the surface at the exact point where the light ray hits. All angles in reflection problems are measured from this normal, not from the surface itself. This is a common mistake on exams.

The law of reflection states:

$\theta_i = \theta_r$

• $\theta_i$ is the angle of incidence, measured between the incoming ray and the normal.
• $\theta_r$ is the angle of reflection, measured between the reflected ray and the normal.

One more geometric fact: the incident ray, the reflected ray, and the normal all lie in the same plane. This means reflection is a 2D problem; you don't need to worry about the light scattering out of that plane.

Example: A light ray strikes a flat mirror at 35° from the normal. The reflected ray leaves at 35° from the normal on the opposite side. If the problem instead gives you the angle from the surface (say, 55°), subtract from 90° first: $90° - 55° = 35°$ from the normal.

Wave Optics and Reflection

Light is an electromagnetic wave, and reflection occurs when these waves encounter a boundary between two media (like air and glass). The law of reflection holds whether you treat light as a wave or as a ray. In this unit, you'll mostly use the ray model, which simplifies the geometry while still giving accurate predictions for mirrors and flat surfaces.

Formation of Images in Plane Mirrors

When light from an object reflects off a plane mirror, the reflected rays diverge as if they originated from a point behind the mirror. Your brain traces those rays straight back and "sees" the object at that point behind the mirror's surface.

A few key properties of plane mirror images:

• Virtual image: The light doesn't actually pass through the image location, so you can't project it onto a screen.
• Upright: The image is right-side up, not flipped top to bottom.
• Laterally inverted: Left and right are swapped. Raise your right hand in front of a mirror, and the image raises its left hand.
• Same size as the object: The image distance behind the mirror equals the object distance in front of it, so there's no magnification.