Reflection
Reflection is the bouncing of a wave, such as light or sound, off a surface; the angle of incidence equals the angle of reflection.
Definition
Reflection is when light or sound bounces off a surface: a mirror reflects light so a person can see their reflection, and a canyon wall reflects sound as an echo, and in fact almost everything is seen by reflection, since the Moon, a book, and a friend's face do not make light but bounce it from the Sun or a lamp into the eye. The law of reflection states that the angle of incidence equals the angle of reflection, both measured from the normal; smooth surfaces produce specular, mirror-like reflection while rough surfaces scatter light diffusely, and sound reflects the same way to produce echoes. This law, $\theta_i = \theta_r$ with the incident ray, reflected ray, and normal coplanar, follows from Fermat's principle of least time and the boundary conditions of Maxwell's equations; the fraction of light reflected at normal incidence between media of indices $n_1$ and $n_2$ is $R = ((n_1 - n_2)/(n_1 + n_2))^2$, about $4\%$ for air-glass, total internal reflection occurs beyond a critical angle $\theta_c = \sin^{-1}(n_2/n_1)$, and curved mirrors obey $1/f = 1/d_o + 1/d_i$ with $f = R/2$.
Example
Shine a flashlight at a mirror and the beam bounces off at the same slant it came in, so tilting the mirror aims it at a chosen spot; a light ray striking a mirror at $35^\circ$ from the normal reflects at $35^\circ$ on the other side, for a total angle of $70^\circ$ between the incoming and outgoing rays, and a shout echoing back in $1.2\ \text{s}$ came from a cliff $343 \times 1.2 / 2 \approx 206\ \text{m}$ away. For glass ($n = 1.50$) to air, $\theta_c = \sin^{-1}(1/1.50) \approx 41.8^\circ$, so light striking an optical fiber's core wall at $80^\circ$ is completely reflected, letting fibers carry signals for kilometers with little loss, and a concave mirror with $R = 40\ \text{cm}$ ($f = 20\ \text{cm}$) and an object at $30\ \text{cm}$ forms a real inverted image at $d_i = 60\ \text{cm}$ from $1/d_i = 1/20 - 1/30$.
Key Insight
A page looks white and a mirror looks like whatever is in front of it, yet both reflect most of the light hitting them: the page scatters it everywhere while the mirror sends each ray in one direction. Reflection off a denser medium flips a wave's phase by $180^\circ$ while reflection from a less dense medium does not, and that phase flip is why a soap film shows colored fringes and why anti-reflective coatings are exactly a quarter wavelength thick.