Physics › 🔦 Optics & Light

Reflection & Refraction

Why a straw looks broken in a glass of water, and why a diamond sparkles more than a puddle.

High schoolAP Physics 2 level
Reflection & Refraction — illustration
Illustrative hero image.
💡
The big idea: Light travels in straight lines until it hits a boundary between two materials. What happens next comes down to one simple fact: light changes speed when it enters a new medium, and that speed change is what bends the ray. Reflection and refraction aren't two unrelated rules — they're both consequences of how light behaves at an interface.
🎯 By the end, you'll be able to
  • explain, using the idea of light changing speed, why a ray bends when it crosses into a new medium
  • calculate an unknown angle of incidence or refraction using Snell's law and given refractive indices
  • find the critical angle for a boundary and predict when total internal reflection will occur
  • state the law of reflection and apply it to mirrors and shiny surfaces
📎 You should already know
  • Basic trigonometry (sine and arcsine)
  • Waves: speed, wavelength, and frequency
  • What a ray diagram and a normal line represent

The straw that isn't really bent

Dip a straw into a glass of water and it looks snapped in half at the surface. The straw is fine — it's the light carrying its image to your eye that changed direction. Every time light crosses from one transparent material into another (air into water, air into glass, water into air), part of it bounces back and part of it bends as it continues on. The bounced part is reflection. The bent part is refraction. Both are happening at once, every time, at every window, puddle, and lens you look through.

🔑 One idea explains both

Reflection: the angle a ray makes with the normal (the imaginary line perpendicular to the surface) coming in equals the angle it makes going out.

Refraction: light bends at a boundary because it changes speed there. Slow down entering a medium, and the ray bends toward the normal. Speed up leaving it, and the ray bends away from the normal. (If there's no change in speed — the same medium on both sides — there's no bending at all.) That's also why a ray hitting a boundary head-on, at 0° incidence, passes straight through undeviated: the light still changes speed as it crosses, but the geometry forces the refracted ray to stay along the same straight line, so there's no direction change to see.

\[ n = \dfrac{c}{v} \]
Refractive index: how many times slower light travels in a medium than in a vacuum. c is the speed of light in vacuum (3.00 × 10⁸ m/s); v is its speed in the medium. n is always ≥ 1.
\[ n_1 \sin\theta_1 = n_2 \sin\theta_2 \]
Snell's law: relates the angles a ray makes with the normal on either side of a boundary, measured from that same normal line — not from the surface itself.
\[ \theta_c = \arcsin\!\left(\dfrac{n_2}{n_1}\right) \]
Critical angle: exists only when light travels from a higher-index medium (n₁) toward a lower-index one (n₂ < n₁). Past this incidence angle, nothing refracts out — the boundary acts like a perfect mirror.
🎮 Interactive: bend the ray yourself LIVE
Drag the incoming ray and change the materials on each side. Watch how the refracted ray swings toward or away from the normal, and find the exact angle where it stops escaping at all — that's the critical angle.

A useful mental picture

Think of marching band members walking from pavement onto sand at an angle. The marchers who hit the sand first slow down while the rest are still cruising on pavement, so the whole line pivots — it bends. Light does the same thing: whichever "side" of the wavefront enters the slower medium first gets held up, and the ray swings toward the normal. Go the other way, from sand back to pavement (slow medium to fast medium), and the ray swings away from the normal instead. You never need to memorize which way it bends — just remember which medium is slower.

📝 Worked example: A light ray in air (n = 1.00) strikes the surface of water (n = 1.33) at an angle of 40° from the normal. Find the angle of refraction.
  1. Write Snell's law: \(n_1 \sin\theta_1 = n_2 \sin\theta_2\)
  2. Plug in values: \((1.00)\sin(40°) = (1.33)\sin\theta_2\)
  3. \(\sin(40°) = 0.643\), so \(0.643 = 1.33\sin\theta_2\)
  4. Solve: \(\sin\theta_2 = 0.643 / 1.33 = 0.483\)
  5. \(\theta_2 = \arcsin(0.483) \approx 28.9°\)
✓ The ray bends toward the normal to about 28.9°, since it's slowing down entering the denser water.
📝 Worked example: Light travels inside water (n = 1.33) and hits the water–air boundary from below. What is the critical angle, and what does it mean physically?
  1. Water is the denser (higher-n) medium here, air is n₂ = 1.00, so a critical angle exists
  2. Use \(\theta_c = \arcsin(n_2/n_1) = \arcsin(1.00/1.33)\)
  3. \(1.00/1.33 = 0.752\)
  4. \(\theta_c = \arcsin(0.752) \approx 48.8°\)
✓ At angles of incidence beyond about 48.8°, no light escapes into the air at all — it all reflects back into the water. This is why looking up from underwater, you only see the sky through a narrow circular window directly overhead; everything beyond that cone is just a mirror-like reflection of the pool itself.
⚠️ Two traps to avoid

Measure from the normal, not the surface. Every angle in these formulas — incidence, reflection, refraction, critical — is measured from the line perpendicular to the boundary, never from the boundary itself.

Total internal reflection only runs one direction. It can only happen when light starts in the higher-index (slower) medium and hits a lower-index (faster) medium — for example, glass-to-air or water-to-air, not the reverse. Going the other way, refraction always finds an exit angle; there's no critical angle to trap it.

Check your understanding

1. According to the law of reflection, for a ray bouncing off a flat mirror, the angle of incidence equals...
The law of reflection states the incoming and outgoing angles, measured from the normal, are equal — this holds for any smooth reflective surface.
2. A ray in air (n = 1.00) enters glass (n = 1.50) at a 30° angle of incidence. What is the angle of refraction, approximately?
sin30° = 0.5, so sinθ₂ = 0.5/1.50 = 0.333, giving θ₂ = arcsin(0.333) ≈ 19.5°. The ray bends toward the normal because glass is denser (slower) than air.
3. Total internal reflection is possible when light travels...
A critical angle — and therefore total internal reflection — only exists when light tries to exit into a medium with a lower refractive index, and only beyond that specific angle.
4. What is the speed of light inside a material with refractive index n = 2.0?
Since n = c/v, v = c/n = (3.00 × 10⁸ m/s)/2.0 = 1.5 × 10⁸ m/s — light travels at half its vacuum speed in this material.
✅ Key takeaways
  • Reflection and refraction both happen at every boundary between transparent media; which one you notice depends on the angle and the materials involved.
  • Refraction is caused by light changing speed — it bends toward the normal when slowing down, away from the normal when speeding up — and is quantified by Snell's law, n₁sinθ₁ = n₂sinθ₂.
  • The refractive index n = c/v tells you how much slower light moves in a material compared to vacuum; larger n means slower light and more bending.
  • Total internal reflection happens only when light moves from a higher-index medium toward a lower-index one, at angles beyond the critical angle θc = arcsin(n₂/n₁).