Difficulty: Introductory | Prerequisites: Basic trigonometry (sine, cosine, inverse trig functions), familiarity with angles measured from a normal line.
This unit introduces the ray model of light and the law of reflection, two foundational ideas that underpin everything from mirrors to lenses later in the course. You need these concepts before tackling refraction, thin lenses, or image formation. If you can draw a ray diagram and apply the law of reflection to a plane mirror, you are ready for the rest of Chapter 18. The material here is conceptual and visual, so spend time sketching diagrams rather than memorising paragraphs.
Light travels in straight lines (rays) as long as openings are larger than about 1 mm. When a ray hits a smooth surface, it bounces off at the same angle it arrived (law of reflection). A plane mirror produces a virtual image the same distance behind the mirror as the object is in front.
Ray
A straight line representing the path light takes through a transparent material or vacuum. The speed of light in a material is v = c/n, where n is the index of refraction. Think of it as an arrow showing which direction the light is heading.
Self-luminous object
An object that creates its own light rays, such as the sun, a light bulb, or a candle flame. In simple terms, it glows on its own.
Reflective object
An object that does not produce its own light but reflects rays that originate from a self-luminous source. Paper, trees, and skin are all reflective objects. Think of it as borrowing someone else's light.
Diffuse reflection
Reflection from a rough surface that sends incident light out in every direction. This is how most ordinary objects (paper, skin, grass) scatter light so that everyone in the room can see them.
Scattering
The process in which a single incident ray is broken into many weaker rays leaving in all directions. In simple terms, the surface sprays the light everywhere instead of bouncing it neatly.
Specular reflection
Reflection from a smooth surface where the angle of incidence equals the angle of reflection, and both rays lie in the same plane. This is the mirror-like bounce you see off glass or polished metal.
Angle of incidence (θ_i)
The angle between the incoming ray and the normal (the perpendicular line) at the point where the ray meets the surface.
Angle of reflection (θ_r)
The angle between the reflected ray and the normal. By the law of reflection, θ_r = θ_i.
Normal
An imaginary line drawn perpendicular to a surface at the point where a ray strikes it. All angles in reflection and refraction are measured from the normal, not from the surface itself.
Virtual image
A point from which reflected (or refracted) rays appear to diverge, but through which no rays actually pass. You cannot project a virtual image onto a screen. Think of it as the image you see "inside" a mirror.
Plane mirror
A flat reflective surface. It produces a virtual image at the same distance behind the mirror as the object is in front: s' = s.
The ray model ignores diffraction. It works whenever the apertures the light passes through are larger than about 1 mm.
Light rays travel in straight lines through a vacuum or any transparent material.
Two rays can cross without affecting each other.
A ray continues forever in a straight line unless it interacts with matter.
At an interface between two materials, light can be reflected, refracted, or both. Within a material, light can be scattered or absorbed.
Self-luminous objects create their own rays (light bulbs, the sun, flames).
Reflective objects redirect rays that originated elsewhere (paper, trees, your hand).
For your eye to see an object, rays from that object must enter the eye. The eye collects a diverging bundle of rays from each point on the object and focuses them onto the retina.
A point source emits rays in every direction. Everyone around it can see it.
An extended source is made up of many point-like sources. All points on it are visible because each point sends rays in all directions.
Most ordinary objects (paper, skin, grass) reflect incident light in every direction. This is diffuse reflection.
Scattering is the process in which a single ray is broken into many weaker rays that leave in all directions. It is why rough surfaces are visible from any angle.
The incident ray, the reflected ray, and the normal all lie in the same plane.
The angle of incidence equals the angle of reflection: θ_i = θ_r.
A single ray in a diagram represents an entire bundle of parallel rays.
A horizontal ray striking the mirror head-on (zero angle of incidence) reflects straight back (zero angle of reflection).
The point P' where the reflected rays appear to diverge from is the virtual image. No rays actually leave P'; the eye simply traces the diverging reflected rays backwards.
The image distance s' equals the object distance s. Written as a relation: s' = s for a plane mirror.
Rays from every point on the object spread out in all directions and hit the mirror. Only a small subset of those reflected rays enter your eye.
Rays from different points on the object (say P and Q) reach your eye after reflecting from different areas of the mirror. This is why a very small mirror may not show you the full image of a large object.
The image in a plane mirror is the same size as the object, upright, and appears to be behind the mirror.
Speed of light in a material:
v = \frac{c}{n}where c is the speed of light in vacuum and n is the index of refraction of the material.
Law of reflection:
\theta_i = \theta_rBoth angles are measured from the normal to the surface.
Plane mirror image distance:
s' = sThe image is virtual, upright, and the same size as the object.
Diffuse reflection is the reason you can read a book from any angle: the page scatters light in all directions, so the text is visible no matter where you sit. Specular reflection is what makes a bathroom mirror work, and it is the same principle behind periscopes and reflecting telescopes.
Students often measure angles from the surface rather than from the normal. All angles in reflection (and later in refraction) are measured from the normal.
Students sometimes think a virtual image means "not real" in the sense that you cannot see it. You can see a virtual image perfectly well; you simply cannot project it onto a screen because no rays actually converge there.
A common mistake is believing that a plane mirror reverses left and right. It does not. It reverses front and back. Your mirror image has the same left and right as you; it is the depth axis that is flipped.
Some students assume you need a mirror the same size as the object to see the full image. A smaller mirror can show the full image if you stand far enough away, because the reflected rays from different parts of the object reach your eye from different parts of the mirror.
⚠️ The law of reflection (θ_i = θ_r, both from the normal) is tested constantly, often as a setup step inside refraction or lens problems.
⚠️ You must be able to distinguish a real image from a virtual image. Plane mirrors always produce virtual images.
⚠️ Know that s' = s for a plane mirror. This relation is simpler than the thin-lens equation but examiners use it as a warm-up or a comparison question.
True or false: the ray model of light is valid when light passes through an opening smaller than 1 mm. (False: the model breaks down below about 1 mm because diffraction effects become significant.)
Fill in the blank: for specular reflection, the angle of ______ equals the angle of ______. (incidence, reflection)
True or false: a virtual image can be projected onto a screen. (False: no rays converge at a virtual image.)
Fill in the blank: for a plane mirror, the image distance s' equals ______. (the object distance s)
True or false: diffuse reflection sends light in every direction, while specular reflection obeys the law of reflection. (True)
Q: A ray of light strikes a plane mirror at an angle of 35° to the surface. What is the angle of reflection?
A: The angle of incidence is measured from the normal, not the surface. 90° minus 35° = 55°. So θ_i = 55°, and by the law of reflection θ_r = 55°.
Q: An object is placed 25 cm in front of a plane mirror. Where is the image, and what type of image is it?
A: The image is 25 cm behind the mirror (s' = s = 25 cm). It is a virtual image, upright, and the same size as the object.
Q: Explain why you can see a white sheet of paper from any direction but you can only see a reflection in a mirror from a specific angle.
A: Paper produces diffuse reflection, scattering light in all directions. A mirror produces specular reflection, so the reflected ray leaves at a definite angle determined by the law of reflection. You only see the reflection when your eye is positioned along that reflected ray.
Q: A student claims that a virtual image is "not real" and therefore invisible. Is this correct?
A: No. A virtual image is visible to the eye. The word "virtual" means that no rays actually converge at the image location. Your eye traces the diverging reflected rays backward and perceives the image as though it were behind the mirror.
The law of reflection reappears when you study concave and convex mirrors (Section 18.6), where the same θ_i = θ_r rule applies at each point on a curved surface. Virtual vs real images is the central distinction you will use throughout the thin-lens and mirror-equation material. Diffuse reflection and scattering connect to wave optics later in the course, where diffraction and interference explain what happens when the ray model breaks down.
Ray model of light, light rays, straight-line propagation, specular reflection, diffuse reflection, scattering, law of reflection, angle of incidence, angle of reflection, normal line, plane mirror, virtual image, image distance, object distance, PHYS 116, University of Washington, general physics optics, Chapter 18 optics