Geometric optics (reflection & refraction)
The idea
Treat light as rays — straight lines that bend only at surfaces — and you can predict mirrors, lenses, and prisms with nothing but geometry. Reflection follows one rule: the angle of incidence equals the angle of reflection, both measured from the normal, the line perpendicular to the surface at the point of impact. Refraction is the bending of light as it crosses into a medium where it travels at a different speed; each medium gets an index of refraction n = c/v, with larger n meaning slower light.
Snell's law governs the bend: n₁ sin θ₁ = n₂ sin θ₂, angles again measured from the normal. Entering a slower medium (larger n), light bends toward the normal; returning to a faster medium it bends away. That second case hides a dramatic effect: beyond a critical angle, where sin θc = n₂/n₁, the refracted ray cannot exist and the light reflects entirely back inside — total internal reflection, the principle that traps light inside optical fibers.
The classic error is measuring angles from the surface itself. Every angle in reflection and refraction is measured from the NORMAL, so a ray skimming nearly parallel to the glass has a large angle of incidence, not a small one. Mislabeling this turns every Snell's law answer upside down.
Worked example
A laser beam in air strikes a glass block (n = 1.52) at 40° from the normal. Find the angle of refraction inside the glass, and then find the critical angle for light trying to leave this glass back into air.
- Apply Snell's law for the entry: n₁ sin θ₁ = n₂ sin θ₂ with n₁ = 1.00 (air), θ₁ = 40°, and n₂ = 1.52.
- Compute the sine: sin 40° = 0.643, so sin θ₂ = 1.00 × 0.643/1.52 = 0.423.
- Take the inverse sine: θ₂ = arcsin(0.423) ≈ 25°. The ray bends toward the normal, as it must when entering a slower, higher-n medium.
- For the exit problem, the critical angle is where the refracted ray would graze the surface at 90°: sin θc = n₂/n₁ = 1.00/1.52 = 0.658.
- Evaluate: θc = arcsin(0.658) ≈ 41°. Light inside the glass hitting the surface at more than about 41° from the normal cannot escape and reflects totally back inside.
- Sanity-check the pair of results: 25° is smaller than 40° (bent toward the normal, correct for air into glass), and a modest 41° critical angle explains why glass and water trap light so readily into internal reflections.
Answer. The beam refracts to about 25° from the normal inside the glass, and the critical angle for glass-to-air is about 41°.
Check your understanding
- Why does light bend toward the normal when it slows down, and how could you predict the bend direction without memorizing it?
- Why does total internal reflection only happen when light travels from a slower medium toward a faster one?
- How does measuring angles from the surface instead of the normal corrupt a Snell's law calculation, and how do you catch the mistake?
- What everyday observations — a bent-looking straw in water, sparkle in a cut gemstone — can you now explain with refraction and the critical angle?
Build the foundations first
Geometric optics (reflection & refraction) builds on these concepts. If any feel shaky, start there.