Преломление
Введено| English | Значение |
|---|---|
| refraction/rɪˈfrækʃn/ | Преломление |
| refractive index/rɪˈfræktɪv ˈɪndeks/ | Показатель преломления |
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:
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Slower in a denser medium, the ray bends toward the normal.
The property $n$ that measures how much a material slows light is its ____.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
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.)
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
$\sin\theta_2 = n_1\sin\theta_1 / n_2 = 0.5 / 1.5 = 0.33$.
Which expresses Snell's law?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Закон Снеллиуса: $n_1\sin\theta_1 = n_2\sin\theta_2$.
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.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Beyond the critical angle the ray can't escape and reflects entirely — total internal reflection.
Select все true statements about refraction.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
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.
Write from a sine of 0.25
- Light goes from air into a medium of refractive index 2.
- The angle in air is 30 degrees and sin 30 degrees is 0.5. Find sin of the angle in the medium.
Light passes from air, refractive index 1, into a medium of refractive index 2. The angle in air is 30 degrees and sin of 30 degrees is 0.5. What is sin of the angle in the medium?
0.5 divided by 2 is 0.25.
What is sin of the angle in the medium?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Index times sine is unchanged, so 0.5 divided by 2 is 0.25. Other options — 0.33 (the lesson glass result); 0.5 (the sine in air left unchanged).