Bending by a rule too
A pencil in a glass of water looks bent at the surface. Light bends there.
- Air above, glass below. The normal is square to the boundary.
- The ray arrives at 40° from the normal, in air.
- It bends towards the normal. The angle in the glass is about 25.4°.
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The rule
Refraction is light bending as it crosses into another material. The angle i is in the first material. The angle r is in the second. Both are measured from the normal. The sine of an angle is written sin. A calculator or a table gives it.
| Law | What it says |
|---|---|
| The bend | Entering an optically denser material, a ray bends towards the normal. Leaving it, the ray bends away. |
| One plane | The incident ray, the refracted ray and the normal lie in one plane. |
| One ratio | For one pair of materials and one colour of light, sin i / sin r is the same at every angle. |
Along the normal, a ray does not bend.
The fixed ratio is the refractive index, n. For light coming from a vacuum, n = c / v. We treat air as a vacuum. Here c is the speed of light in a vacuum. And v is its speed in the material. This v is a speed, not an image distance.
| Material | n |
|---|---|
| Water | 1.33 |
| Glass | 1.5 |
| Diamond | 2.42 |
A material with a bigger n is optically denser. This is not the same as heavier. Since n = c / v, a bigger n means slower light.
Worked example
A ray enters glass, n = 1.5, from air at i = 40°.
The law says sin i / sin r = n. So sin r = sin i / n. The sine of 40° is 0.643.
sin r = sin i / n = 0.643 / 1.5 = 0.428, so r ≈ 25.4°. That is the angle whose sine is 0.428. A calculator finds it.
Light in glass is slower: v = c / 1.5. With c = 3 × 10⁸ m/s, v = 2 × 10⁸ m/s.
Send a ray back along the bent path. It goes back out along the first path.