Refraction
Refraction is the bending of a wave as it passes from one medium into another at an angle, caused by a change in the wave's speed.
Definition
Refraction is the bending of light as it moves from one material into another, like from air into water, because the light changes speed and that change in speed changes its direction; a straw in a glass of water looks bent at the surface because the light from its underwater part bends before reaching the eye, and a fish in a pond looks closer to the surface than it really is for the same reason. Light bends toward the normal when it slows down entering a denser medium and away from the normal when it speeds up leaving one, its frequency staying the same while wavelength and speed change, and lenses, prisms, rainbows, and mirages all depend on it. Refraction obeys Snell's law, $n_1\sin\theta_1 = n_2\sin\theta_2$, where refractive index $n = c/v$ measures how much a medium slows light, following from Fermat's principle and the continuity of wavefronts across a boundary; because $n$ depends on wavelength, with blue bending more than red in glass, a prism spreads white light into a spectrum, and for a thin lens, refraction at both surfaces yields the lensmaker's equation and the thin-lens relation $1/f = 1/d_o + 1/d_i$.
Example
Light travels at $3.00 \times 10^8\ \text{m/s}$ in air but only $2.25 \times 10^8\ \text{m/s}$ in water, so a beam hitting a pool at $45^\circ$ from the normal bends to about $32^\circ$ inside the water, while a beam hitting straight down slows but does not bend at all. Light entering water ($n = 1.33$) from air at $45^\circ$ refracts to $\sin\theta_2 = \sin 45^\circ / 1.33 \approx 0.532$, so $\theta_2 \approx 32.1^\circ$, and in crown glass, where $n = 1.514$ for red ($656\ \text{nm}$) and $1.524$ for blue ($486\ \text{nm}$), a $45^\circ$ beam refracts to $27.83^\circ$ and $27.64^\circ$ respectively, a $0.19^\circ$ spread that a prism's second surface then widens.
Key Insight
Refraction bends light because one edge of the beam slows before the other, the way a shopping cart veers when one wheel rolls onto grass: no angle, no veer. A rainbow packs refraction, reflection, and dispersion into one raindrop, light bending in, reflecting off the back, and bending again leaving, with red exiting at about $42^\circ$ and violet at $40^\circ$ from the anti-solar point, so every observer sees a private rainbow made by a different set of drops.