Difficulty: Introductory | Prerequisites: Basic trigonometry (sine, cosine, inverse trig functions), comfort with angles and right triangles.
This chapter introduces the foundational models for understanding light: how it travels, how it bounces off surfaces, and how it bends when passing between materials. These ideas underpin everything from how your eyes work to how lenses and mirrors form images. You should already be comfortable with basic trigonometry and angle measurement. If you can handle Snell's law, you can handle the rest of optics that follows in later chapters.
Light travels in straight lines (rays) until it hits something. When it hits a smooth surface, it reflects at equal angles (law of reflection). When it crosses from one material into another, it bends (refraction), and the amount of bending is governed by Snell's law. Total internal reflection happens when light tries to leave a denser medium at too steep an angle and gets trapped inside.
Ray
A straight line representing the path along which light travels. Think of it as an arrow showing the direction a beam of light moves.
Point source
An infinitely small source that emits light rays in all directions. In simple terms, it is a source so small that its size does not matter for ray-tracing purposes.
Extended source
A light source whose entire surface emits light; every point on the surface acts as its own point source. A fluorescent tube or the sun (as seen from Earth) are everyday examples.
Specular reflection
Reflection from a smooth surface where all incoming parallel rays bounce off in the same direction, preserving the image. This is what mirrors do.
Diffuse reflection
Reflection from a rough surface where each tiny patch obeys the law of reflection, but because the surface is uneven, the reflected rays scatter in many directions. This is why you can see a white wall from any angle but it does not show your reflection.
Normal
The line perpendicular to a surface at the point where a ray strikes it. All angles in reflection and refraction are measured from this line, not from the surface itself.
Angle of incidence (θ_i)
The angle between the incoming ray and the normal at the point of contact.
Angle of reflection (θ_r)
The angle between the reflected ray and the normal. By the law of reflection, θ_r = θ_i.
Refraction
The bending of a light ray as it crosses the boundary between two transparent media with different indices of refraction. In simple terms, light changes direction because it changes speed.
Index of refraction (n)
A dimensionless number describing how much slower light travels in a material compared with a vacuum: n = c / v. A higher n means slower light and more bending.
Snell's law
n₁ sin θ₁ = n₂ sin θ₂. The quantitative rule that tells you exactly how much a ray bends at a boundary.
Critical angle (θ_c)
The angle of incidence beyond which all light is reflected back into the denser medium instead of crossing the boundary. It exists only when light moves from a higher-n to a lower-n material.
Total internal reflection (TIR)
The complete reflection of light at a boundary when the angle of incidence exceeds the critical angle. This is the principle behind fibre optics.
Virtual image
An image formed where reflected or refracted rays appear to diverge from, but do not actually pass through. Your reflection in a flat mirror is a virtual image: it looks like it is behind the glass, but no light is actually there.
Scattered light
Light that hits a surface and breaks into many weaker rays heading in random directions (diffuse reflection at a microscopic level). This is how you can see most objects around you.
The ray model treats light as a collection of straight lines radiating outward from a source. It is a simplification, but it works extremely well for predicting shadows, reflection and refraction.
Five key assumptions of the ray model
Light rays travel in straight lines.
Light rays can cross one another without interacting.
A ray travels forever in a straight line unless it interacts with matter (reflection, refraction, absorption).
An object is a source of light rays (either emitting its own or reflecting/scattering light from another source).
The eye sees by collecting and focusing a bundle of rays; rays must enter the eye for us to see something.
Point source vs extended source
A point source is infinitely small and emits rays in all directions. Everyone can see a point source because it sends light everywhere.
An extended source has a finite surface. Every point on that surface acts as its own little point source, emitting rays in all directions. All points of an extended source are visible from any angle.
Shadows
A point source creates sharp shadows with well-defined edges, because rays either reach a region or they do not.
An extended source creates shadows with a fuzzy boundary. The fully blocked region (umbra) receives no light at all. The partially blocked region (penumbra) receives light from some points on the source but not others.
Scattered light (diffuse reflection)
When a ray strikes a rough surface, it breaks into many weaker rays that head off in random directions.
Some of those scattered rays enter your eye, which is why you can see objects that do not glow on their own.
Every visible point on a non-luminous object is scattering light toward you.
When light hits a surface and bounces back, it reflects. The details depend on whether the surface is smooth or rough.
Law of reflection
The angle of incidence equals the angle of reflection: θ_i = θ_r.
Both angles are measured from the normal (the line perpendicular to the surface at the point of contact), not from the surface.
The incident ray, the reflected ray and the normal all lie in the same plane.
Specular reflection
Occurs on smooth surfaces (mirrors, polished metal, still water).
Parallel incoming rays all reflect in the same direction, preserving the spatial relationship of the rays. This is why you see a clear image.
Diffuse reflection
Occurs on rough or textured surfaces (paper, painted walls, fabric).
Each tiny patch of surface still obeys θ_i = θ_r locally, but because the surface normal points in a different direction at each patch, the reflected rays scatter in many directions.
You can see the surface from any viewing angle, but you do not see a mirror image.
Mirrors and virtual images
A flat (plane) mirror produces a virtual image that appears to be the same distance behind the mirror as the object is in front.
The image point P' is located where the reflected rays, extended backward, appear to converge.
The image is the same size as the object and is upright (not inverted top to bottom), but it is left-right reversed.
The image is called "virtual" because no actual light passes through P'. Your eye simply interprets diverging reflected rays as if they came from a point behind the mirror.
When a ray crosses the boundary between two transparent materials (say, air into glass), part of the light reflects and part continues into the new medium. The transmitted ray changes direction. That change of direction is refraction.
Why light bends
Light travels at different speeds in different materials. The speed of light in a medium is v = c / n, where c is the speed in a vacuum and n is the index of refraction.
A higher index of refraction means a slower speed and more bending.
Snell's law
n₁ sin θ₁ = n₂ sin θ₂
n₁ and n₂ are the indices of refraction of the two media. θ₁ is the angle of incidence (in medium 1), θ₂ is the angle of refraction (in medium 2).
When a ray enters a medium with a higher n, it bends toward the normal (θ₂ < θ₁).
When a ray enters a medium with a lower n, it bends away from the normal (θ₂ > θ₁).
Total internal reflection (TIR)
TIR can only occur when light travels from a higher-n medium into a lower-n medium (for example, glass into air).
As the angle of incidence increases, the refracted ray bends further from the normal. At the critical angle θ_c, the refracted ray skims along the boundary (θ₂ = 90°).
Beyond θ_c, no light crosses the boundary at all; it is entirely reflected back into the denser medium.
The critical angle is found from Snell's law: sin θ_c = n₂ / n₁ (with n₁ > n₂).
TIR does not occur when light moves from a lower-n to a higher-n medium. There is no critical angle in that direction.
Law of reflection: θ_i = θ_r
Index of refraction: n = c / v, where c = 3.0 × 10⁸ m/s (speed of light in vacuum) and v is the speed in the medium.
Snell's law: n₁ sin θ₁ = n₂ sin θ₂
Critical angle for TIR: sin θ_c = n₂ / n₁ (only valid when n₁ > n₂)
Speed of light in a medium: v = c / n
Relationship between v and Snell's law: (c / v₁) sin θ₁ = (c / v₂) sin θ₂, which simplifies to (sin θ₁) / v₁ = (sin θ₂) / v₂
Total internal reflection is the principle behind fibre-optic cables: light enters a thin glass fibre and bounces along its length without escaping, carrying data over long distances with very little loss. Specular reflection is what makes everyday mirrors, car wing mirrors and telescopes work. Refraction is why a swimming pool looks shallower than it really is, and why a straw in a glass of water appears to bend at the surface.
Students often measure the angle of incidence from the surface rather than from the normal. All reflection and refraction angles are measured from the normal.
Students sometimes think diffuse reflection breaks the law of reflection. It does not. Each micro-patch of a rough surface obeys θ_i = θ_r; the surface is simply uneven, so the normals point in different directions.
A common error is assuming that total internal reflection can happen when light goes from a less dense to a more dense medium (low n to high n). TIR only occurs when light moves from higher n to lower n.
Students confuse virtual images with imaginary or non-existent images. A virtual image is perfectly visible to your eye; the word "virtual" only means the light rays do not actually pass through the image location.
⚠️ Snell's law calculations are a near-certainty on any optics exam. Be comfortable rearranging n₁ sin θ₁ = n₂ sin θ₂ for any unknown.
⚠️ You will likely be asked to calculate the critical angle for a given pair of materials.
⚠️ Expect ray diagrams: drawing incident rays, normals, reflected rays and refracted rays with correct angles.
⚠️ Know the sign convention: angles from the normal, not from the surface.
⚠️ Virtual image problems (flat mirrors) are common: the image distance equals the object distance, measured behind the mirror.
True or false: The angle of reflection is measured from the surface, not from the normal. (False – it is measured from the normal.)
Fill in the blank: When light enters a medium with a higher index of refraction, it bends ______ the normal. (toward)
True or false: Total internal reflection can occur when light passes from air into glass. (False – TIR only occurs going from higher n to lower n.)
Fill in the blank: The critical angle formula is sin θ_c = ___. (n₂ / n₁, where n₁ > n₂)
True or false: A virtual image in a flat mirror is the same size as the object. (True)
Q: A ray of light in air (n = 1.00) strikes a glass surface (n = 1.50) at an angle of incidence of 30°. What is the angle of refraction?
A: Using Snell's law: (1.00)(sin 30°) = (1.50)(sin θ₂). sin θ₂ = 0.50 / 1.50 = 0.333. θ₂ = sin⁻¹(0.333) ≈ 19.5°. The ray bends toward the normal because it enters a denser medium.
Q: What is the critical angle for light travelling from glass (n = 1.50) into air (n = 1.00)?
A: sin θ_c = n₂ / n₁ = 1.00 / 1.50 = 0.667. θ_c = sin⁻¹(0.667) ≈ 41.8°. Any angle of incidence greater than 41.8° produces total internal reflection.
Q: Explain why diffuse reflection does not violate the law of reflection.
A: Each microscopic patch of a rough surface has its own local normal. The law of reflection (θ_i = θ_r) holds at every patch, but because the normals point in different directions across the surface, the reflected rays scatter in many directions rather than forming a single reflected beam.
Q: An object stands 25 cm in front of a flat mirror. Where does the virtual image appear, and what is its size relative to the object?
A: The virtual image appears 25 cm behind the mirror (image distance equals object distance for a plane mirror). The image is the same size as the object and is upright.
Q: Can total internal reflection occur when light travels from water (n = 1.33) into diamond (n = 2.42)? Why or why not?
A: No. TIR requires light to travel from a higher-n medium to a lower-n medium. Water has a lower n than diamond, so no critical angle exists for that boundary.
The ray model and Snell's law are the foundation for everything that follows in optics: image formation by lenses and mirrors (Sections 18.4 to 18.7), optical instruments (microscopes, telescopes), and the wave model of light (diffraction, interference). The index of refraction also connects to the electromagnetic wave speed in a material, tying this chapter to electromagnetism. Understanding virtual and real images here is essential before tackling the thin lens equation and mirror equation in the second half of this chapter.
Ray optics, geometric optics, light ray, law of reflection, specular vs diffuse reflection, mirror image, virtual image, plane mirror, refraction of light, Snell's law, index of refraction, refractive index, critical angle, total internal reflection, TIR, fibre optics, bending of light, transmitted ray, normal line, angle of incidence, angle of refraction, point source, extended source, shadow, umbra, penumbra, scattered light, diffuse reflection