Part of OP-02 — Wave Optics

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A wavefront is the locus of points in the same phase, and Huygens' principle — every wavefront point acts as a new secondary source — provides the geometric basis for deriving Snell's law. In Young's double slit experiment, two coherent slits separated by dd at distance DD from a screen produce equally spaced fringes of width β=λD/d\beta = \lambda D/d. Bright fringes form where the path difference equals a whole number of wavelengths (Δ=nλ\Delta = n\lambda), and dark fringes form at odd half-wavelength differences (Δ=(2n1)λ/2\Delta = (2n-1)\lambda/2). The intensity at any point is I=4I0cos2(ϕ/2)I = 4I_0\cos^2(\phi/2), giving Imax=4I0I_{\max} = 4I_0 and Imin=0I_{\min} = 0 for identical slits. Coherent sources must share the same frequency and a constant phase difference; two independent bulbs or even two separate lasers cannot sustain a visible fringe pattern. Single slit diffraction produces a central maximum of width 2λD/a2\lambda D/a, which is twice as wide as secondary maxima, and minima at asinθ=nλa\sin\theta = n\lambda. Polarization proves light is a transverse wave — its electric field oscillates perpendicular to the propagation direction and can be restricted to one plane by a polaroid. Brewster's law states tanθp=n\tan\theta_p = n; at this angle the reflected ray is completely plane-polarized and perpendicular to the refracted ray. Malus's law gives the intensity of polarized light through an analyser: I=I0cos2θI = I_0\cos^2\theta, yielding zero through crossed polaroids and I0/8I_0/8 when a third polaroid is inserted at 45°45°. In any medium of refractive index nn, the wavelength shortens to λ/n\lambda/n and the fringe width shrinks proportionally to β/n\beta/n.

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