Refraction
Introduced| English |
|---|
| refraction/rɪˈfrækʃn/ |
| refractive index/rɪˈfræktɪv ˈɪndeks/ |
A straw in a glass looks snapped in half
- Drop a straw into a glass of water and it appears bent at the surface.
- The straw is fine — it's the light that bends as it crosses from water to air.
- Light changes direction when it moves between materials — refraction 折射.
- It happens because light travels at different speeds in different media.
Why light bends
- Light moves slower in a denser medium (glass, water) than in air.
- Entering a slower medium, a ray bends toward the normal; leaving it, away from the normal.
- The bending is set by each material's refractive index 折射率 $n$ (higher $n$ = slower light).
- Air is about $n = 1$; water $\approx 1.33$; glass $\approx 1.5$.
Bend a ray at a boundary
Change the angle and medium and watch the ray bend toward or away from the normal.
Entering a denser medium (like glass), a light ray bends:
Slower in a denser medium, the ray bends toward the normal.
The property $n$ that measures how much a material slows light is its ____.
A higher refractive index means light travels slower in that material.
Snell's law
- The angles and indices are linked by Snell's law: $n_1\sin\theta_1 = n_2\sin\theta_2$.
- Angles are measured from the normal, as always in optics.
- Going into a denser medium ($n_2 > n_1$) makes $\theta_2 < \theta_1$ — the ray bends toward the normal.
- Snell's law predicts exactly how much a ray bends at any boundary.
Light goes from air ($n_1 = 1$) into glass ($n_2 = 1.5$) at $\theta_1 = 30^\circ$ ($\sin 30^\circ = 0.5$). What is $\sin\theta_2$? (Give a decimal.)
$\sin\theta_2 = n_1\sin\theta_1 / n_2 = 0.5 / 1.5 = 0.33$.
Which expresses Snell's law?
Snell's law: $n_1\sin\theta_1 = n_2\sin\theta_2$.
Total internal reflection
- Going the other way (dense to less dense), the ray bends away from the normal.
- Past a critical angle, it can't escape at all and reflects entirely back inside.
- This total internal reflection traps light in optical fibres and sparkles in diamonds.
- It is refraction taken to its extreme — no light gets out.
Past the critical angle, light going from glass to air is totally internally reflected.
Beyond the critical angle the ray can't escape and reflects entirely — total internal reflection.
Select all true statements about refraction.
Refraction is a speed effect obeying Snell's law; a ray along the normal ($\theta = 0$) does not bend at all.
Refraction bends light because its speed changes between media — not because it "wants to". Light bends toward the normal entering a denser (slower, higher-$n$) medium, and away from it leaving one. A ray hitting the boundary straight along the normal ($\theta_1 = 0$) does not bend.
Light passes from air ($n_1 = 1$) into glass ($n_2 = 1.5$) at $\theta_1 = 30^\circ$. Find $\sin\theta_2$.
- Snell: $1 \times \sin 30^\circ = 1.5 \times \sin\theta_2 \Rightarrow \sin\theta_2 = \dfrac{0.5}{1.5} = 0.33$.
Since $\sin\theta_2 < \sin\theta_1$, the ray bends toward the normal, as expected for a denser medium.
Refraction bends light at a boundary because its speed changes; it bends toward the normal entering a denser (higher-$n$) medium. Snell's law: $n_1\sin\theta_1 = n_2\sin\theta_2$. Past a critical angle, dense-to-rare light undergoes total internal reflection — the basis of optical fibres.