Reflection and Refraction

Objective: Use incident and reflected angles relative to a normal.

In a ray model of specular reflection from a smooth surface, angle of incidence equals angle of reflection when both are measured from the surface normal. A ray striking at 30° from the normal reflects at 30° on the other side of the normal. Diffuse reflection from a rough surface still follows local reflection at small facets but scatters rays in many directions. A mirror’s image is formed by the geometry of reflected rays, not by light emerging from behind the mirror. Ray diagrams are useful when wavelength is small compared with structures; wave behavior becomes important in other regimes. Distinguish angles from the normal versus from the surface.

Objective: Explain bending from speed changes and use a simple index model.

Refraction is a change in propagation direction as a wave crosses a boundary where its speed changes, except at normal incidence where direction need not bend. Refractive index n = c/v for light in a medium under stated wavelength and conditions. For light passing from air into a medium with larger n, the ray generally bends toward the normal; frequency remains set by the source, while speed and wavelength change. Snell’s law n₁ sinθ₁ = n₂ sinθ₂ gives ray angles in suitable media. A medium with n = 1.5 gives v ≈ 2.0 × 10⁸ m/s from c/n. Dispersion occurs because n varies with wavelength, so different colors can bend by different amounts.

Objective: Interpret reflected and transmitted color under specified illumination.

An object’s perceived color depends on the spectrum illuminating it, how its material absorbs, reflects, or transmits wavelengths, and the observer’s visual response. A red-looking opaque object under broad white light reflects relatively more red wavelengths; under illumination lacking red, it may appear dark. An ideal red filter transmits red light and absorbs or reflects much of other visible light, but real filters are not perfect. White light is a mixture of visible wavelengths; a prism separates wavelengths by dispersion rather than creating colors from nothing. Pigment mixing differs from additive mixing of emitted light, so context matters. Color alone cannot establish chemical composition uniquely.