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.