Wave Optics

Where Chapter 9 treated light as rays, this chapter reveals it as a wave — a compact, concept-dense scorer worth 4-7 Board marks and 1-2 questions in JEE/NEET. The story begins with the corpuscular-vs-wave debate (Descartes and Newton vs Huygens), settled by Young's 1801 interference experiment and Foucault's 1850 speed measurement. Huygens' principle — every point of a wavefront is a source of secondary wavelets whose envelope is the new wavefront — derives both the law of reflection and Snell's law, predicting correctly that light slows in denser media ($\frac{\sin i}{\sin r} = \frac{v_1}{v_2}$, with wavelength shrinking and frequency unchanged). Superposing coherent waves gives interference: path difference $n\lambda$ for bright ($I = 4I_0$), $(n+\frac{1}{2})\lambda$ for dark, while incoherent sources merely add intensities ($2I_0$). Young's double slit converts this into measurable, equally spaced fringes of width $\beta = \lambda D/d$ — the experiment that measured light's wavelength. A single slit produces diffraction: a broad central maximum with minima at $\theta = n\lambda/a$ and weakening secondary maxima at $(n+\frac{1}{2})\lambda/a$ — with Feynman's reminder that interference and diffraction differ only in usage. Finally, polarisation proves light's transverse nature: polaroids, the half-intensity rule for unpolarised light, Malus' law $I = I_0\cos^2\theta$ and the crossed-polaroid experiments. Every derivation, formula and exam-favourite condition is covered.