Short on time? This page is the recap. For explanations, the three figures and the worked examples, use the full study guide.
Recap
- Refraction is the change in direction of a ray as it passes from one medium into another.
- It happens because the speed of light changes at the boundary. The frequency does not change.
- A ray that meets the boundary along the normal slows down but does not bend.
- Into a higher n: bends toward the normal. Into a lower n: bends away from the normal.
- Total internal reflection (TIR): going into a lower n, beyond the critical angle, all the light reflects and none is transmitted. At exactly θc the refracted ray runs along the surface.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| n = c / v | c = 3.00 × 10⁸ m/s; n has no units | find the speed of light in a medium, or n from a speed |
| n₁ sin θ₁ = n₂ sin θ₂ | θ measured from the normal, in degrees | find a refracted angle or an unknown n |
| sin θc = n₂ / n₁ | only when n₁ > n₂ | find the critical angle for TIR |
| sin θ_air = n sin θ_material | slope of sin θ_air vs sin θ_material = n | find n from a graph of experimental data |
Assumptions behind the numbers
- Air has n = 1.00 (its real value, 1.0003, makes no difference at three significant figures).
- Each medium is uniform, so rays travel in straight lines inside it.
- Light is treated as rays; its wave nature is ignored in this topic.
- Thin container walls with parallel faces do not change the final direction of a ray.
Mistakes to avoid
- Angle from the surface. Always use the angle from the normal.
- Wrong way round in Snell’s law. Pair each n with the angle in the same medium.
- Calculator in radians. Check that sin 30 = 0.5.
- TIR in the wrong direction. It can only happen going into a lower n.
- Plotting θ₂ against θ₁ and expecting a straight line. Plot the sines.
- Saying light “speeds up into glass”. Higher n means lower speed.
Quick self-check
- Light travels at 2.40 × 10⁸ m/s in a plastic. What is n? (1.25)
- Find the critical angle for glass (n = 1.52) to air. (41.1°)
- A ray in air meets water (n = 1.33) at 45°. What is the angle of refraction? (32.1°, toward the normal)
- Can a ray in air be totally internally reflected at a water surface? (No: going into a higher n, the refracted angle is always smaller than the incident angle.)
Next: practice questions.