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 at distance from a screen produce equally spaced fringes of width . Bright fringes form where the path difference equals a whole number of wavelengths (), and dark fringes form at odd half-wavelength differences (). The intensity at any point is , giving and 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 , which is twice as wide as secondary maxima, and minima at . 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 ; 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: , yielding zero through crossed polaroids and when a third polaroid is inserted at . In any medium of refractive index , the wavelength shortens to and the fringe width shrinks proportionally to .
Part of OP-02 — Wave Optics
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