Formula grid
| Quantity | Equation | Units |
|---|---|---|
| Wave speed | $v=f\lambda$ | m/s, Hz, m |
| Period | $T=1/f$ | s, Hz |
| Refractive index | $n=\sin i/\sin r$ | °, no unit for $n$ |
| Critical angle | $\sin c=1/n$ | ° |
Transverse
Oscillations perpendicular to energy transfer. EM, water, rope.
Longitudinal
Oscillations parallel to energy transfer. Sound: compressions and rarefactions.
EM spectrum (increasing $f$)
Radio · micro · IR · visible (ROYGBIV) · UV · X-ray · gamma. All $3.0\times 10^8\,\text{m/s}$ in vacuum.
- Radio: comms · Micro: cooking / satellite · IR: heaters / night vision
- Visible: fibres / photography · UV: fluorescent lamps
- X-ray: internal structure · Gamma: sterilising
- Hazards: micro — internal heating; IR — burns; UV — cells / blindness; gamma — cancer / mutation
TIR checklist
- Denser → rarer (glass to air)
- $i > c$
$i=r$ still. Fibres and 45° prisms use this.
Traps
- Angles from the normal, never from the surface.
- Convert cm, kHz, MHz before $v=f\lambda$.
- Sound is longitudinal. EM is transverse.
- $n=\sin i/\sin r$, not the other way up.
- Doppler: observed $f$ and $\lambda$ change; source $f$ does not.
- Both TIR conditions, not just $i>c$.