Optics and Light

Reflection and Refraction

Reflection returns light at the incident angle. Refraction bends light between media according to Snell's law: $n_1\sin\theta_1 = n_2\sin\theta_2$ Light bends toward the normal entering a denser (higher $n$) medium and away leaving it. Above the critical angle ($\sin\theta_c = n_2/n_1$, slow-to-fast only), total internal reflection traps the light — the principle behind fiber optics and endoscopes.

Lenses and Mirrors

The thin lens and mirror equation with magnification governs all image formation: $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}, \qquad m = -\frac{d_i}{d_o}$ Converging lenses and concave mirrors have positive $f$; diverging lenses and convex mirrors negative. Positive $d_i$ means a real, inverted image; negative means virtual and upright. Lens power in diopters is $P = 1/f$ (meters); myopia is corrected with diverging lenses, hyperopia with converging.

Light as a Wave and Particle

The EM spectrum runs radio to gamma with $c = f\lambda$; visible light spans roughly 400-700 nm. Diffraction and interference show wave behavior, while the photoelectric effect ($E = hf$, ejection only above a threshold frequency) shows particle behavior.

Key Takeaways

• Higher index means slower light and bending toward the normal.
• One equation plus sign conventions solves every lens/mirror problem.
• Real images are inverted; virtual images are upright.
• Photon energy depends on frequency, not intensity.