Geometric Optics

When the wave nature of light doesn't matter, you can model light as rays, straight lines perpendicular to the wavefronts that point the way the light travels, and draw ray diagrams to follow them. A reflected ray leaves a surface at the same angle it arrived, with both angles measured from the normal (an imaginary line at right angles to the surface). A smooth surface gives specular reflection in one direction, while a rough surface gives diffuse reflection that scatters light in many directions.

A concave mirror is converging: rays parallel to its axis reflect through the focal point, about halfway between the mirror and its center of curvature. A convex mirror is diverging, so reflected rays only seem to come from a focal point behind it, and a plane mirror makes an image as far behind it as the object is in front. You find an image with three principal rays or with $\frac{1}{s_o} + \frac{1}{s_i} = \frac{1}{f}$ and its sign conventions, then describe it as real or virtual, upright or inverted, and larger, smaller or the same size.

Refraction is the bending of light as it crosses into a new medium, and it happens because light changes speed. The index of refraction is $n = \frac{c}{v}$, and Snell's law, n₁ sin θ₁ = n₂ sin θ₂, tells you the new angle: light bends toward the normal going into a higher index and away from it going into a lower index. Going from a higher to a lower index, rays hitting the boundary beyond the critical angle undergo total internal reflection, with no light transmitted at all.

A thin convex lens is converging: rays parallel to its axis bend toward a focal point on the far side. A thin concave lens is diverging: those rays spread out as if they came from a focal point on the near side. Lenses use the same thin-lens equation, $\frac{1}{s_o} + \frac{1}{s_i} = \frac{1}{f}$, and the same three principal rays as mirrors, so you can find where an image forms, whether it's real or virtual, and its size and orientation.