Waves, Sound, and Optics

The wave equation

Every wave obeys $v=f\lambda$, linking speed, frequency, and wavelength. Increasing frequency while speed stays fixed (as in a single medium) means wavelength must shrink to compensate.

Sound and echoes

Sound is a mechanical wave that needs a medium to travel through. An echo is a reflected sound wave; since the sound travels to the reflecting surface and back, the distance to that surface is $d=\frac{vt}{2}$, where $t$ is the total time from emission to hearing the echo.

Reflection and refraction of light

The law of reflection says the angle of incidence equals the angle of reflection. Refraction is the bending of light as it crosses into a different medium, governed by Snell's law: $n=\frac{\sin i}{\sin r}$, where $i$ is the angle of incidence and $r$ is the angle of refraction, both measured from the normal.

Mirrors and lenses

The mirror/lens formula relates object distance $u$, image distance $v$, and focal length $f$: $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$. Magnification is $m=\frac{v}{u}$.

Total internal reflection

This happens only when light travels from a denser medium towards a less dense one, at an angle beyond the critical angle $C$, where $\sin C=\frac{1}{n}$.