The same equation again
The slope, and the two directions that make it easy
An inclined plane looks like a harder problem than a flat one. Split the weight into two components chosen to suit the slope and it becomes an easier one.
WavesA wave is a shape that travels, and nothing else does
In a wave on water, no water goes anywhere. What moves is the shape — and separating the two motions is the whole of wave physics.
WavesWhen two waves meet, they simply add
Waves pass through each other unchanged and their displacements add point by point. From that one impoverished-sounding rule comes interference, beats, and the evidence that light is a wave at all.
WavesOnly some notes fit, and that is where discreteness comes from
A string clamped at both ends can vibrate at some frequencies and not others. A continuous object producing a whole-number list is the oldest quantisation in physics.
OpticsThe bend at the boundary, and what it is really about
Light changes direction when it changes speed. Snell's law is the geometry of that statement, and it can be derived without knowing anything about light at all.
OpticsWhat a lens is doing, and why three rays are enough
A lens bends every ray that reaches it. The construction uses three, because three are all that can be drawn without calculation — and any three that meet prove all the rest do.
OpticsThe angle past which light cannot leave
Snell's law asks for the sine of an angle greater than one, and no such angle exists. What happens instead is a perfect mirror made out of nothing but a change of speed.