What is refraction and why does light bend?
Refraction is the change in the direction of light when it passes at an angle from one transparent medium to another, such as from air into water or glass. It happens because light travels at different speeds in different media: about 3 × 10⁸ m/s in air, about 2.25 × 10⁸ m/s in water, about 2 × 10⁸ m/s in glass.
A medium in which light is slower is called optically denser; one in which it is faster is optically rarer. Optical density is not the same as mass density: kerosene is lighter than water yet optically denser.
- Rarer → denser (air into glass): light slows and bends toward the normal (r < i).
- Denser → rarer (glass into air): light speeds up and bends away from the normal (r > i).
- If light falls along the normal (i = 0°), it does not bend at all, although its speed still changes.
Laws of refraction (Snell's law)
- First law: the incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
- Second law (Snell's law): for light of a given colour and a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.
sin i / sin r = constant = n₂₁
The constant is the refractive index of the second medium with respect to the first. In story step 3 you can see i and r both change while the ratio stays fixed.
Refractive index
The refractive index tells how much a medium slows light, and so how much it bends light.
Relative refractive index
For light going from medium 1 into medium 2:
n₂₁ = speed of light in medium 1 / speed of light in medium 2 = v₁/v₂
Absolute refractive index
When medium 1 is vacuum (or air, practically the same):
n = c / v
Since light is fastest in vacuum, n is always greater than 1 for any material. It has no unit. Also n₂₁ = n₂/n₁ and n₁₂ = 1/n₂₁.
| Medium | n (approx.) |
|---|---|
| Air | 1.0003 |
| Water | 1.33 |
| Kerosene | 1.44 |
| Crown glass | 1.52 |
| Diamond | 2.42 |
Diamond has one of the highest values, which is part of why it sparkles so much.
Refraction through a rectangular glass slab
A ray hitting a glass slab bends twice: toward the normal at the first face (air → glass) and away from the normal at the second face (glass → air).
- Because the two faces are parallel, the bending at the second face exactly undoes the first. So the emergent ray is parallel to the incident ray and the angle of emergence e equals the angle of incidence i.
- The emergent ray is, however, shifted sideways. This perpendicular distance between the incident ray (extended) and the emergent ray is the lateral displacement.
- The lateral shift grows when the slab is thicker, when i is larger and when the refractive index is larger. At i = 0° there is no shift.
This is the classic lab activity: trace a slab, fix pins along a ray, and measure i, r and e with a protractor.
Refraction in daily life and board-exam pointers
- A tank or pond looks shallower than it is (apparent depth < real depth).
- A pencil partly in water looks bent at the surface.
- Letters seen through a thick glass slab look raised.
- Stars twinkle because starlight passes through air layers of changing refractive index.
What is asked: the two laws, the definition of refractive index and n = c/v numericals (1–3 marks), which medium is optically denser from a table, and the glass slab ray diagram with e = i and lateral displacement (2–3 marks).
Key formulas and definitions
- sin i / sin r = n₂₁ (Snell's law)
- n₂₁ = v₁ / v₂ = n₂ / n₁
- Absolute refractive index: n = c / v, with c = 3 × 10⁸ m/s
- n₁₂ = 1 / n₂₁
- Glass slab: angle of emergence e = angle of incidence i
Worked examples
1. The refractive index of glass is 1.5. Find the speed of light in glass.
v = c/n = (3 × 10⁸)/1.5 = 2 × 10⁸ m/s.
2. Light travels at 2.25 × 10⁸ m/s in a liquid. Find the liquid's refractive index.
n = c/v = (3 × 10⁸)/(2.25 × 10⁸) = 1.33 (this is water).
3. n of water = 1.33 and n of glass = 1.5. Find the refractive index of glass with respect to water.
n(glass w.r.t. water) = n_glass / n_water = 1.5/1.33 ≈ 1.13.
4. A ray enters a medium of refractive index √2 (≈ 1.414) from air at 45°. Find the angle of refraction.
sin r = sin i / n = sin 45° / √2 = (1/√2)/√2 = 1/2, so r = 30°.
5. A ray falls at 60° on a glass slab of refractive index √3. Find the angle of refraction inside and the angle of emergence.
sin r = sin 60°/√3 = (√3/2)/√3 = 1/2, so r = 30°. The faces are parallel, so the ray leaves at e = i = 60°, parallel to the incident ray.
6. In which is light faster, glass (n = 1.5) or diamond (n = 2.42)? Find the speed in diamond.
Speed is c/n, so the smaller n (glass) is faster. In diamond v = 3 × 10⁸/2.42 ≈ 1.24 × 10⁸ m/s, while in glass it is 2 × 10⁸ m/s.
7. Light goes from water (n = 1.33) into glass (n = 1.5) at an angle of incidence of 30°. Find the angle of refraction.
Snell's law for two media: n₁ sin i = n₂ sin r. sin r = 1.33 × 0.5 / 1.5 ≈ 0.443, so r ≈ 26.3°. It bends toward the normal because glass is optically denser than water.
Common mistakes
- Saying light always bends toward the normal. It bends toward the normal only when it enters a denser medium; it bends away when leaving it.
- Thinking a ray falling along the normal (i = 0°) bends. It goes straight, though its speed changes.
- Confusing optical density with mass density (kerosene floats on water but is optically denser).
- Giving refractive index a unit, or a value below 1. It is a ratio of speeds, has no unit and is at least 1 for any material.