The messenger we see with
Almost everything you know about the world beyond arm's reach arrived as light. Look up and you receive light that left the Sun eight minutes ago, or a star thousands of years ago. Three plain facts about light will carry us a long way. First, in a uniform medium light travels in straight lines — this is why you get sharp shadows and why you can aim a laser pointer. Second, it is astonishingly fast: about 3\times10^{8} metres per second in vacuum, fast enough to circle the Earth seven times in one second. Third, it carries energy — sunlight warms your skin, and a strong enough beam can cut steel.
Optics is the study of how light behaves: how it bounces, bends, spreads, and combines. Remarkably, a huge fraction of what you meet daily — mirrors, lenses, rainbows, fibre-optic internet, the very act of seeing — falls out of just a handful of rules that we can build from scratch in this track.
Two pictures: the ray and the wave
Physicists carry two mental pictures of light and switch between them. In the ray model (geometric optics), light is a set of thin straight arrows that reflect and bend at surfaces. This picture is simple and it is exactly what you need for mirrors, lenses, cameras and eyes. In the wave model (physical optics), light is a travelling wave that can spread around obstacles, add up and cancel out. You need this picture for interference, diffraction and colour effects in thin films.
Light is an electromagnetic wave
What is actually waving? Not a rope, not air — light needs no medium and crosses empty space. Light is an electromagnetic wave: a self-sustaining ripple of electric and magnetic fields, oscillating at right angles to each other and to the direction of travel. Because it needs no medium, it sails through the vacuum of space at the universal speed c. A wave is described by its wavelength \lambda (the distance between crests) and its frequency f (cycles per second). For light these two are locked together by the wave speed relation.
For light in vacuum, frequency times wavelength equals c. Since c is fixed, a shorter wavelength always means a higher frequency.
One spectrum, many faces
Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays are all the same thing — electromagnetic waves — differing only in wavelength and frequency. Radio waves can be metres or kilometres long; visible light spans roughly 400 nm (violet) to 700 nm (red); gamma rays are shorter than an atomic nucleus. What we casually call the colour of light is simply its wavelength. The full family is the electromagnetic spectrum, and the sliver our eyes respond to is no accident: it is exactly where the Sun is brightest and where water is transparent.
Reflection: the first law of optics
When light hits a smooth surface it bounces. Draw an imaginary line perpendicular to the surface at the point of contact — the normal. Measure the incoming ray's angle from this normal (call it \theta_i) and the outgoing ray's angle from it (\theta_r). The law of reflection says these are equal, and both rays plus the normal lie in one plane.
Angle of incidence equals angle of reflection — both measured from the normal, never from the surface itself.
The law holds even for a rough wall — but there each tiny facet points a different way, so parallel incoming rays scatter every which way. That is diffuse reflection, and it is why you see a matte page from any angle. A polished mirror keeps the facets aligned (specular reflection), so parallel rays stay parallel and an image survives. Same law, different surfaces.