A boundary changes the path.
Reflection obeys equal angles of incidence and reflection, measured from the normal. Refraction occurs when wave speed changes across a boundary. Frequency stays fixed by the source while wavelength changes.
Refractive index n = c/v. Snell’s law connects indices and ray angles. Total internal reflection requires travel from a higher to a lower refractive index and an incidence angle above the critical angle; below that angle some light can refract out.
Glass to air
Explore the relationship
Angles from the normal. A 90° boundary means the critical angle has been reached; beyond it there is no transmitted ray (total internal reflection).
Tap or focus a plotted point to read its values.
View plotted data as a table
| Series | Incidence angle / degrees | Refracted angle / degrees |
|---|---|---|
| Refracted angle / degrees | 0 | 0 |
| Refracted angle / degrees | 0.666667 | 1.00003 |
| Refracted angle / degrees | 1.33333 | 2.00023 |
| Refracted angle / degrees | 2 | 3.00076 |
| Refracted angle / degrees | 2.66667 | 4.00181 |
| Refracted angle / degrees | 3.33333 | 5.00354 |
| Refracted angle / degrees | 4 | 6.00612 |
| Refracted angle / degrees | 4.66667 | 7.00974 |
| Refracted angle / degrees | 5.33333 | 8.01456 |
| Refracted angle / degrees | 6 | 9.02078 |
| Refracted angle / degrees | 6.66667 | 10.0286 |
| Refracted angle / degrees | 7.33333 | 11.0381 |
| Refracted angle / degrees | 8 | 12.0497 |
| Refracted angle / degrees | 8.66667 | 13.0634 |
| Refracted angle / degrees | 9.33333 | 14.0794 |
| Refracted angle / degrees | 10 | 15.0981 |
| Refracted angle / degrees | 10.6667 | 16.1195 |
| Refracted angle / degrees | 11.3333 | 17.144 |
| Refracted angle / degrees | 12 | 18.1718 |
| Refracted angle / degrees | 12.6667 | 19.2031 |
| Refracted angle / degrees | 13.3333 | 20.2382 |
| Refracted angle / degrees | 14 | 21.2773 |
| Refracted angle / degrees | 14.6667 | 22.3208 |
| Refracted angle / degrees | 15.3333 | 23.369 |
| Refracted angle / degrees | 16 | 24.4221 |
| Refracted angle / degrees | 16.6667 | 25.4806 |
| Refracted angle / degrees | 17.3333 | 26.5447 |
| Refracted angle / degrees | 18 | 27.6148 |
| Refracted angle / degrees | 18.6667 | 28.6915 |
| Refracted angle / degrees | 19.3333 | 29.775 |
| Refracted angle / degrees | 20 | 30.8659 |
| Refracted angle / degrees | 20.6667 | 31.9646 |
| Refracted angle / degrees | 21.3333 | 33.0718 |
| Refracted angle / degrees | 22 | 34.188 |
| Refracted angle / degrees | 22.6667 | 35.3138 |
| Refracted angle / degrees | 23.3333 | 36.4499 |
| Refracted angle / degrees | 24 | 37.5971 |
| Refracted angle / degrees | 24.6667 | 38.7562 |
| Refracted angle / degrees | 25.3333 | 39.9281 |
| Refracted angle / degrees | 26 | 41.1138 |
| Refracted angle / degrees | 26.6667 | 42.3144 |
| Refracted angle / degrees | 27.3333 | 43.5312 |
| Refracted angle / degrees | 28 | 44.7655 |
| Refracted angle / degrees | 28.6667 | 46.019 |
| Refracted angle / degrees | 29.3333 | 47.2932 |
| Refracted angle / degrees | 30 | 48.5904 |
| Refracted angle / degrees | 30.6667 | 49.9127 |
| Refracted angle / degrees | 31.3333 | 51.2628 |
| Refracted angle / degrees | 32 | 52.6438 |
| Refracted angle / degrees | 32.6667 | 54.0594 |
| Refracted angle / degrees | 33.3333 | 55.5139 |
| Refracted angle / degrees | 34 | 57.0125 |
| Refracted angle / degrees | 34.6667 | 58.5616 |
| Refracted angle / degrees | 35.3333 | 60.1692 |
| Refracted angle / degrees | 36 | 61.8454 |
| Refracted angle / degrees | 36.6667 | 63.6034 |
| Refracted angle / degrees | 37.3333 | 65.4607 |
| Refracted angle / degrees | 38 | 67.4421 |
| Refracted angle / degrees | 38.6667 | 69.5837 |
| Refracted angle / degrees | 39.3333 | 71.9426 |
| Refracted angle / degrees | 40 | 74.6186 |
Explore: Increase the glass-to-air incidence angle through the critical angle.
Light enters glass (n = 1.5) normally from air.
- At normal incidence both angles are 0°, so the ray does not bend.
- Speed falls to c/1.5 and wavelength decreases, but frequency stays fixed.
Assumed knowledge
Sine and inverse sine in degrees.
Learning checkpoints & source
YOUR LEARNING CHECKPOINT- Apply reflection and Snell’s law.
- Explain total internal reflection and critical angle.