Refraction

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: Apply refraction to calculations, evidence, and specified situations.

Refractive index is n=c/v. At a stationary boundary, Snell’s law n1sinθ1=n2sinθ2 relates angles from the normal. Frequency remains fixed while speed and wavelength change. Total internal reflection requires travel from higher to lower index and incidence above the critical angle, where sinθ_c=n_low/n_high. These ray relations assume the specified transparent media and geometrical-optics conditions. Rounding inside trigonometric calculations should be delayed until the final angle.